nga-logo3
 

 


NGA.SIG.0014_0.2_PROJRAS

 

 

 

 

 

 

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY (NGA)

STANDARDIZATION DOCUMENT

Implementation Practice

 

Map Projections for Tiled Raster Graphics

 

 

2015-01-28

 

Version 0.2

 

 

 

OFFICE OF GEOMATICS

 

 


Table of Contents

 

1.         Scope......................................................................................................................................   1

2.         Authority.................................................................................................................................   1

3.         References..............................................................................................................................   1

4.         Background.............................................................................................................................   2

5.         Tiled Mercator ......................................................................................................................   4

6.         Tiled Transverse Mercator.....................................................................................................   6

7.         Tiled Polar Stereographic ......................................................................................................   7

8.         Summary..............................................................................................................................   10

 

 

 

 

Appendices

A1.    Scale....................................................................................................................................   A-1

A2.    Tiled Mercator zoom-levels scale sets...............................................................................   A-1

A3.    Tiled transverse Mercator zoom-levels scale sets.............................................................   A-2

A4.    Tiled polar stereographic zoom-levels scale sets...............................................................   A-2

A5.    The universal zoom-levels scale set...................................................................................   A-2

A6.    Tiled Mercator, again.........................................................................................................   A-4

A7.    Tiled transverse Mercator, again.......................................................................................   A-6

A8.    Tiled polar stereographic, again........................................................................................   A-6

 

 

 

List of Tables

Table 1 – Universal zoom-levels scale set.................................................................................   A-3

Table 2 – Tiled Mercator zoom-levels scale set.......................................................................   A-8

Table 3 – Tiled transverse Mercator zoom-levels scale set..................................................   A-13

Table 4 – Tiled polar stereographic zoom-levels scale set....................................................   A-24

 

 


1. Scope

 

This document specifies the map-projections and tile-pyramids that are authorized for maps and imagery produced as zoom-able tiled raster-graphics.  Formerly, the “web-Mercator” and Plate Carrée projections were considered appropriate for this purpose.  This document specifies what should be used instead.  These terms are explained below.

 

This document treats raster-graphics exclusively.  Vector graphics (feature data) are not covered.  This document assumes that the raster graphics conform to one of the commonly used device-independent formats, such as PNG, JPEG, JPEG2000, BMP, etc.

 

This document is written especially for the developers of data and software for mobile and hand-held devices (e.g. “smart phones”) who will be adopting the OGC GeoPackage Encoding Standard (see 3.10) and the related implementation interoperability standard (see 3.11), but is not limited to those devices, applications, and software environments.

 

 

2. Authority

 

The National Geospatial-Intelligence Agency (NGA) serves as the Functional Manager for GEOINT to the National System of Geospatial-Intelligence (NSG).  As such, NGA is responsible for specifying coordinate systems and map-projections that are consistent with the World Geodetic System of 1984 and suitable for the broad range of NSG usages, including navigation, targeting, simulations, mission planning, and geographic analysis. 

 

As the NSG Functional Manager for GEOINT, NGA issued NGA.SIG.0011_1.0_WEBMERC, “Web Mercator Map Projection” forbidding the use of “web-Mercator” (also called pseudo-Mercator and other names) “for the acquisition, visualization, exploitation, and exchange of any GEOINT data for the NSG”.  By the same authority, this document now specifies what should be used in place of web-Mercator for tiled raster graphics.

 

NGA.SIG.0011_1.0_WEBMERC was adopted by the Department of Defense (DoD) Information Technology Standards and Profile Registry (DISR) in August, 2014.

 

 

3. References

 

            3.1 Department of Defense Directive 5105.60 (DoDD 5105.60), “Subject:  National Geospatial-Intelligence Agency (NGA)”, July 29, 2009

 

            3.2 MIL-STD-2401, Department of Defense Standard Practice “Department of Defense World Geodetic System (WGS)”, 11 January 1994

 

            3.3 CJCSI 3900.01C, “Position (Point and Area) Reference Procedures”, 30 June 2007

            3.4 CJCSI 6130.01E, “2013 CJCS Master Positioning, Navigation, and Timing Plan (MPNTP)”, 1 May 2013

 

            3.5 NGA.STND.0036_1.0_WGS84, "Department of Defense World Geodetic System 1984, Its Definition and Relationships With Local Geodetic Systems", Fourth Edition [formerly NIMA Technical Report TR8350.2]

 

            3.6 NGA.SIG.0011_1.0_WEBMERC, “Web Mercator Map Projection”

 

            3.7 NGA.SIG.0012_2.0.0_UTMUPS, “The Universal Grids and the Transverse Mercator and Polar Stereographic Map Projections”

 

            3.8 USGS Professional Paper:1395, “Map Projections: A Working Manual”, Snyder, John P., 1987

 

            3.9 OGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2 – June 2013

 

            3.10 OGC GeoPackage Encoding Standard, OCG 12-128r10, approval date 2014-01-19.

 

            3.11 NGA.IP.xxxx_x.x, National System for Geospatial Intelligence (NSG) GeoPackage Encoding Standard 1.0 Implementation Interoperability Standard (DRAFT)

 

 

4. Background

 

            4.1 All modern display devices are, in simple terms, raster devices.  The display portion of a television, computer, tablet, or smart-phone is organized as rows and columns of square dots called pixels or rasters.  The file formats, PNG, JPEG, etc., are device-independent abstractions of the display hardware.  The mapping of pixels in the file to pixels of the display hardware is an important engineering problem, but is outside the scope of this document.  This document pertains to the raster graphics file.

 

            4.2 Rasters and vectors are different ways to organize the same graphical information.  There are many graphical elements; a line segment will illustrate the difference.  In vector graphics, a line segment consists of the coordinates of the endpoints, a code (typically an integer) for the line style (solid, dashed, dash-dotted etc.), a code (typically an integer or short list of integers) for the color, and a code or number for the line thickness.  In raster graphics, a line segment is the collection (subset) of all the pixels that depict it.  The set of pixels may be colorized or monochrome; they won’t be contiguous if the line is not solid. 

 

            4.3 Raster graphics and vector graphics (feature data) may be included together in a geopackage.  A geopackage is a container format analogous to the way a ZIP file is a container for files of disparate formats.  References 3.10 and 3.11 specify the required and allowed contents of a geopackage.  This document is concerned solely with the raster graphics components of geopackages.

            4.4 Raster graphics can be tiled or untiled.  NGA’s program to scan paper maps and charts and make them available digitally yields untiled raster graphics – typically one large JPEG2000 file for the entire sheet.  Internet-accessible road maps such as Google Maps are tiled raster graphics.  Mouse-ing over an area of interest in Google Maps and performing Save As will yield a PNG file for the tile that contains the point selected.   There is no entire sheet.  There are many tiles.  This document pertains exclusively to tiled raster graphics.

 

            4.5 The operation of selecting a portion of a tiled raster graphic, and re-displaying it at larger scale is called “zooming-in”.  The reverse is “zooming-out”.  Zooming-in can happen two ways:  (i) Using the same file (PNG, JPEG, other), the file pixels are mapped to a greater number of device pixels than before.  The same symbols and labels are shown, enlarged; feature selection is unchanged.  Or, (ii) using another file (PNG, JPEG, other), new detail is portrayed; symbols and labels are changed or re-sized relative to the features.  In this document, zooming, zoom-able, and zoom levels refer to the latter process, i.e. (ii).   

 

4.6 In accordance with References 3.10 and 3.11, a tile is 256 pixels wide by 256 pixels tall, making all tiles are square in shape.  This is true for every zoom-level.  Columns of pixels and columns of tiles are numbered from left to right.  Rows of pixels and rows of tiles are numbered from top to bottom. 

 

            4.7 Also in accordance with References 3.10 and 3.11, there are at least 25 zoom levels, numbered 0, 1, 2, 3, … 24.  Zoom level 0 is the extreme of zooming-out.   Zoom level  has tiles across and tiles up (or down).  Zoom level  covers the same portion of the Earth as zoom level  but with twice as many tiles (in each direction) and therefore, presumably, twice as much detail.  The collection of all tiles for all zoom-levels is called the tile pyramid.

 

4.8 A map, chart, or piece of imagery requires a map-projection.  A map-projection is the procedure, usually mathematical, by which points on an ellipsoid model of the Earth are either (i) assigned to pixels in a raster-graphics product, or (ii) assigned to rectangular coordinatesin a plane.  The number pairs  can be utilized in vector-graphics and grid coordinates, as well as ingredients to procedure (i).  This document is concerned mainly with (i) and partly with (ii) as a means to accomplish (i).

 

4.9 Web-Mercator is a map-projection based on the controversial idea that the proper formulas for the Mercator projection of the WGS 84 ellipsoid should be shortened (modified) in a particular way for (i) ease of implementation and (ii) efficiency of the early primitive hand-held devices.  It should not be used for either raster or vector graphics.  See Reference 3.6.  Web-Mercator has code EPSG::3857 and is also called pseudo-Mercator.

 

4.10 Plate Carrée is a map projection based on the simple idea that  should be the longitude (in decimal degrees, say) and  should be the latitude in the same units.  ESRI’s ArcGIS software calls this scheme “Unprojected” indicating that it is merely the option by default (“I didn’t think about choosing a map-projection”).  This document allows Plate Carrée for vector graphics (feature data), but prohibits it for tiled raster graphics.  Plate Carrée has the code EPSG::4326.

5. Tiled Mercator

 

This section specifies “tiled Mercator”.  It is the (standard) ellipsoidally-correct Mercator projection modified slightly for zoom-able tiled raster graphics.  The modifications – scale and origins – reflect the fact that Mercator as raster graphics is a different species than Mercator as paper map or Mercator as world-wide grid coordinates.

 

The details are divided into several subsections:  ellipsoid parameters, forward mapping equations, and inverse mapping equations.

 

            5.1 Ellipsoid parameters

 

The WGS 84 ellipsoid shall be employed, and its parameters shall be computed as follows:

 

           

 

The names of these constants are:  semi-major axis (), inverse flattening (), flattening (), eccentricity-squared (), and eccentricity ().  It is unfortunate that the eccentricity and the base of the natural logarithms use the same letter .  In this document, the latter usage, , will be notated

 

            5.2 Forward mapping equations

 

For zoom level , the equations to convert longitude (, in radians) and latitude (, in radians) to pixel column number (, counting from the left) and pixel row number (, counting down from the top) are:

 

Notes:

 

One radian is degrees.  (“lambda”) is required to lie in the interval , which in degrees is the interval from  to  (“phi”) is required to lie in the interval defined by the inequality, .  In degrees, this works out to as the extremes of allowed latitude.   The function is the inverse hyperbolic tangent.  is the greatest integer less than or equal to .   is the leftmost pixel column and  is the rightmost pixel column, counting continuously across tile boundaries, which occur every 256 pixels.    is the topmost pixel row and  is the bottommost pixel row, counting continuously across tile boundaries, which occur every 256 pixels.  

 

 

            5.3 Inverse mapping equations

 

For zoom level , the equations to convert pixel column number () and pixel row number () to longitude () and latitude ()  are:

 

 

where

 

Notes

 

A pixel is not a geometric point.  In the above procedure, its center is adopted as its pinpoint position.   is the inverse sine (“arcsin”); is the hyperbolic tangent; and is the exponential function to the base given by Euler’s number,   

 

 

6. Tiled transverse Mercator

 

This section specifies “tiled transverse Mercator”.  It is the (standard) ellipsoidally-correct transverse Mercator projection modified slightly for zoom-able tiled raster graphics.  The modifications – scale and origins – reflect the fact that transverse Mercator as raster graphics is a different species than transverse Mercator as paper map (e.g. TLM50’s) or transverse Mercator as grid coordinates (e.g. UTM coordinates).

 

The details are divided into several subsections:  ellipsoid parameters, transverse Mercator constants, central meridian, forward mapping equations, and inverse mapping equations.

            6.1 Ellipsoid parameters

 

See Section 5.1, above.

 

            6.2 Transverse Mercator constants

 

See section 3.2 of NGA.SIG.0012_2.0.0_UTMUPS for the values of constants  and see Section 3.5 of the same document for the values of constants .  The number is the radius of a semi-circle having the same arclength as a meridian.  The notation  is chosen to follow the notations, ,, and, for various Earth-radii defined by Helmut Moritz’s article, Geodetic Reference System 1980, and repeated in NGA.STND.0036_1.0_WGS84

 

            6.3 Central meridian

 

Let be the longitude (in radians) of the central meridian.  Its degree equivalent must be an integer that is divisible by 3 but not by 2.  In other words, it must be one of the values allowed for Universal Transverse Mercator (UTM) coordinates.

 

            6.4 Forward mapping equations

 

Let  and  be the functions defined in Section 3.2 of NGA.SIG.0012_2.0.0_UTMUPS.  For zoom level , the equations to convert longitude (, in radians) and latitude (, in radians) to pixel column number (, counting from the left) and pixel row number (, counting down from the top) are:

 

Notes:

 

One radian is degrees.  Consistent with the Notes to Section 5.2,  is the greatest integer less than or equal to  is the leftmost pixel column, and  is the rightmost pixel column counting continuously across tile boundaries, which occur every 256 pixels.   Also consistent with the Notes to Section 5.2,  is the topmost pixel row and  is the bottommost pixel row, counting continuously across tile boundaries, which occur every 256 pixels.

 

(“lambda”) is required to lie in the interval , and  (“phi”) is required to lie in the interval  but there is a further restriction.  It is required that at least one of the following must be true:   must be within radians (i.e. ) of either the central meridian () or the anti-central meridian () , or  must be within radians (i.e. ) of either the North Pole or the South Pole.   This is discussed also in Section 3.7 of NGA.SIG.0012_2.0.0_UTMUPS

 

            6.5 Inverse mapping equations

 

Let  and  be the functions defined in Section 3.5 of NGA.SIG.0012_2.0.0_UTMUPS.  For zoom level , the equations to convert pixel column number () and pixel row number () to longitude () and latitude ()  are:

 

 

Notes: 

 

A pixel is not a geometric point.  In the above procedure, its center is adopted as its pinpoint position.  For ease of reading the above formulas, note that functions  and  take the same two arguments in the same order. 

 

 

7. Tiled polar stereographic

 

This section specifies “tiled polar stereographic”.  It is the (standard) ellipsoidally-correct polar stereographic projection modified in a particular way for zoom-able tiled raster graphics.  The modifications – scale and origins – reflect the fact that polar stereographic as raster graphics is a different species than polar stereographic as paper maps (e.g. some aeronautical charts) or polar stereographic as grid coordinates (e.g. UPS coordinates).  This section gives the north polar stereographic. 

 

The details are divided into several subsections:  ellipsoid parameters, polar stereographic constants, polar stereographic parameters, forward mapping equations, and inverse mapping equations.

 

            7.1 Ellipsoid parameters 

 

These are the same as those as in Section 5.1, above.

 

            7.2 Polar stereographic constants

 

See section 8.1 of NGA.SIG.0012_2.0.0_UTMUPS for the value of the constant

            7.3 Polar stereographic parameters

 

The allowed values for the central meridian (, in radians) are .  The degree equivalents are  There will be two special latitudes. The first is a standard parallel chosen to be radians (i.e. ).  From this is obtained the following scale reduction factor:

 

 

 

where function is defined in Section 8.1 of NGA.SIG.0012_2.0.0_UTMUPS.  The second special latitude will refer to the parallel circle that is tangent to the boundaries of the level-0 tile.  This is discussed later.

 

            7.4 Forward mapping equations

 

Let  and  be the functions defined in Section 8.1 of NGA.SIG.0012_2.0.0_UTMUPS.  For zoom level , the equations to convert longitude (, in radians) and latitude (, in radians) to pixel column number (, counting from the left) and pixel row number (, counting down from the top) are:

 

For the NORTH polar stereographic projection,

 

 

For the SOUTH polar stereographic projection,

 

 

 

 

Notes:

 

One radian is degrees.  Consistent with the Notes to Section 5.2,  is the greatest integer less than or equal to  is the leftmost pixel column, and  is the rightmost pixel column counting continuously across tile boundaries, which occur every 256 pixels.   Also consistent with the Notes to Section 5.2,  is the topmost pixel row and  is the bottommost pixel row, counting continuously across tile boundaries, which occur every 256 pixels.

 

The arithmetic indicated in the above formulas can be performed, as follows:

 

 

 

(“lambda”) is required to lie in the interval , and  (“phi”) is required to lie in the interval , and these further restrictions apply:

 

 

Note that the inequalities for  and  are strict in a different place.

 

            7.5 Inverse mapping equations

 

Let  and  be the functions defined in Section 8.2 of NGA.SIG.0012_2.0.0_UTMUPS.  For zoom level , the equations to convert pixel column number () and pixel row number () to longitude () and latitude ()  are:

 

 

For the NORTH polar stereographic projection,

 

 

 

 

 

For the SOUTH polar stereographic projection,

 

 

Notes: 

 

A pixel is not a geometric point.  In the above procedures, its center is adopted as its pinpoint position.  For ease of reading the above formulas, note that for NORTH and separately for SOUTH, the functions  and  take the same two arguments in the same order. 

 

For NORTH polar stereographic, the parallel circle tangent to the boundaries of the level-0 tile is 25.0560°S, computed by the expression, .   For SOUTH, it is 25.0560°N

 

8. Summary

 

NGA and DoD require that mobile and hand-held devices employ a tiled map-projection within a short list of options.  The specifications above, namely tiled Mercator, tiled transverse Mercator and tiled polar stereographic, are that short list.

 

The forgoing sections make a complete specification.  The appendices that follow are informative.

 

 

 

 

 

 

 

 

 

 

 

 

 

(This page is intentionally blank)


 

nga-logo3
 

 


NGA.SIG.0014_0.2_PROJRAS

 

 

 

 

 

 

NATIONAL GEOSPATIAL-INTELLIGENCE AGENCY (NGA)

STANDARDIZATION DOCUMENT

Implementation Practice

 

Map Projections for Tiled Raster Graphics

 

 

Appendices

 

 


A1. Scale

 

Beginning here, several sections are devoted to the subject of scale; they provide information about the scale of the tiled map-projections (raster graphics) specified above.  Scale is as important to raster graphics as it is to paper maps or grid coordinates, but, of necessity, it is specified differently for raster graphics than for the others.

 

A1.1 The scale of raster graphics is typically stated as a number of meters/pixel (“meters per pixel”).  For example, tiled Mercator, at zoom level 10 and latitude 11° has the value 150.084 meters/pixel, found in Table 2.  This means that one pixel on the map corresponds to 150.084 meters on the ground at that latitude.

 

A1.2 Strictly speaking, the number 150.084 meters/pixel is reciprocal scale not scale.  This is explained by an analogy with paper maps.  One cm on the map corresponds to 50,000 cm on the ground, in the case of NGA’s product “TLM50”.  The scale is , not 50,000.  The number 50,000 is the reciprocal scale.  Scale is always and reciprocal-scale is always the inverse ratio.  In the case of raster graphics, the unit of “map distance” is the pixel.  Also, “on the ground” means “on the Earth” and this is short for “on the ellipsoid model of the Earth”.

 

A1.3 Meters/pixel is reciprocal scale.  Understanding this will make the tables more intuitive.  In Table 2, heading north to Greenland, where the scale is understood to be larger, corresponds to smaller values for meters/pixel.

 

A1.4 The scale and reciprocal scale depend on the zoom-level and the location on Earth.  For tiled Mercator and tiled polar stereographic, the location needs only the latitude; the longitude can be ignored.  For tiled transverse Mercator, the location needs both the latitude and the longitude.

 

A1.5 A zoom-levels scale set is the listing of meters/pixel for every zoom-level at a particular point (or relatively small area containing the point).  It is location dependent.  Said another way, specifying a zoom-levels scale set always begs the question of where the zoom-levels scale set is true.

 

 

A2. Tiled Mercator zoom-levels scale sets

 

Meters/pixel for tiled Mercator are tabulated in Table 2 for every zoom level n and every degree of latitude (within range).  The latitudes,  and  have the same value for meters/pixel; it suffices to publish tables for the northern hemisphere only.

 

The tables were computed using this formula:

 

reciprocal scale

A3. Tiled transverse Mercator zoom-levels scale sets

 

Meters/pixel for tiled transverse Mercator are tabulated in Table 3 for every zoom level n, every 5° of latitude from the Equator to 85°N and every 1° of longitude from the central-meridian to central-meridian plus 10°.  Because of symmetry, it suffices to publish tables for one quadrant only (East of the central meridian; north of the Equator).

 

The tables were computed using this formula:

 

reciprocal scale

 

where

f3 refers to the function defined in section 6.3 of NGA.SIG.0012_2.0.0_UTMUPS

 

 

A4. Tiled polar stereographic zoom-levels scale sets

 

Meters/pixel for the tiled polar stereographic projection are tabulated in Table 4 for every zoom level and every 1° of latitude from the Pole to the Equator.  Because of symmetry, it suffices to publish the tables for the NORTH polar stereographic only.

 

The tables were computed using this formula:

 

reciprocal scale  meters/pixel

 

where

 f3 refers to the function in section 8.1 of NGA.SIG.0012_2.0.0_UTMUPS, and

 

           

 

 

A5. The universal zoom-levels scale set

 

This section restates the scale properties of the tiled map-projections defined in this document. 

 

A5.1 Paper maps offer a helpful analogy.  Without changing the scale, there is more than one way to report the scale.  On the walls of NGA hang copies of a world map on the Mercator projection.  The stated scale is 1:22,000,000 at the Equator, appropriate for a world map showing both hemispheres.  Yet, it would be equally valid to state the scale as 1:11,000,000 at latitude 60° (because and few decimals are specified).  The scale could be so restated; only the margin note would change; no rework by the cartographer would be required.

 

A5.2 In the summer and fall of 2014, the DoD inter-agency discussions that led to the specifications in this document formulated the following loose requirement.  If possible, a zoom-level should have the same meaning across all map-projections and over the entire globe.  This is impossible on both counts, but it did lead to the idea of a universal zoom-levels scale set, which roughly meets this requirement to some extent.

 

A5.3 The universal zoom-levels scale set is stated below.  The specification of where it is true for each tiled map-projection will follow.

 

Zoom Level

Meters/pixel

0

134217.728

1

67108.864

2

33554.432

3

16777.216

4

8388.608

5

4194.304

6

2097.152

7

1048.576

8

524.288

9

262.144

10

131.072

11

65.536

12

32.768

13

16.384

14

8.192

15

4.096

16

2.048

17

1.024

18

0.512

19

0.256

20

0.128

21

0.064

22

0.032

23

0.016

24

0.008

Table 1.  Universal zoom-levels scale set

 

The meters/pixel value for zoom level  is .  The numbers in the above table are exact.  In millimeters, they are powers of two, i.e. millimeters for zoom level n.  At zoom level 27, if the table were extended that far, the (reciprocal) scale would be one millimeter per pixel, appropriate to make an image of a survey marker’s inscriptions.

 

A5.4 For tiled Mercator (Section 5), the localities where the universal zoom-levels scale set (Section A5.3) is true are latitudes ±31.0606963703645°

 

A5.5 For tiled transverse Mercator (Section 6), the locality where the universal zoom-levels scale set (Section A5.3) is true is not simple.  There is no curve of constant latitude or constant longitude that defines it.  Instead two accurate points are given along with the approximate principle that the locality of true scale is found at points the same distance from the central meridian as these two points. 

 

Point 1 lies on the Equator at 30.700524332812° of longitude east of the central meridian.

 

Point 2 sits at longitude central meridian plus 90° and co-latitude 30.84537358066145°.

 

The above points lie in the quadrant north of the Equator and east of the central meridian.  The other quadrants have symmetrically placed points of true scale.

 

A5.6 For the tiled polar stereographic projection (Section 7), the locality where the universal zoom-levels scale set (Section A5.3) is true is 31° of latitude from the Pole, exactly.  For the NORTH polar stereographic, this means latitude 59°N.   For the SOUTH, this means latitude 59°S.

 

A5.7 The universal zoom-levels scale set serves another purpose.  It provides (at every zoom level) a discretization of the map-projection plane in a manner independent of the choice of the map-projection.  Let zoom level 24 be an example.  The plane is discretized as little squares, 0.008 meters on a side.  The squares become the pixels and all tiling details are decided by this.  Choice of map-projection and its parameters, within classical treatments like John P. Snyder’s Map Projections: A Working Manual or NGA’s NGA.SIG.0012_2.0.0_UTMUPS, would be the only remaining matters for the construction of new (or the above) tiled map-projections. 

 

 

A6. Tiled Mercator, again

 

This section re-states the forward mapping equations for tiled Mercator, taking inspiration from the universal zoom-levels scale set.  Previously given equations (Section 5) were unencumbered by intermediate grid coordinates , i.e. the conversion was simply from  to . Here we introduce and re-arrange some constants (multipliers) so that  to  conforms to classical treatments (see section A5.7) and to is generically given, i.e. independent of the map-projection and its parameters (again see section A5.7). 

 

            A6.1 The forward mapping equations are:

 

 

 

            where

 and n is the zoom level.

 

The computation that determines  is: 

 

            A6.2 The EPSG operation-method-code for the above  to  conversion is EPSG::9804 with these values for its required parameters:

·        

·        

·          is the above

·         FE

·         FN

 

            A6.3 The current Well-Known-Text format (as of 2014 December) for the above EPSG parameters, copied from NGA.IP.xxxx_x.x, National System for Geospatial Intelligence (NSG) GeoPackage Encoding Standard 1.0 Implementation Interoperability Standard (DRAFT), is the following:

 

·         PROJECTION["Mercator_variant_A", AUTHORITY["EPSG","9804"]],

·         PARAMETER["Latitude of natural origin",0],

·         PARAMETER["Longitude of natural origin",0],

·         PARAMETER["Scale factor at natural origin", 0.857385503731176],

·         PARAMETER[“False easting”,0],

·         PARAMETER[“False northing”,0],           

 

            A6.4 The new proposed Well-Known-Text format for the above EPSG parameters, copied from the same document, is the following:

 

·         METHOD[“Mercator (variant A)”,ID[“EPSG”,”9804”]],

·         PARAMETER[“Latitude of natural origin”,0, ANGLEUNIT[“degree”,0.0174532925199433]],

·         PARAMETER[“Longitude of natural origin”,0,

ANGLEUNIT[“degree”,0.0174532925199433]],

·         PARAMETER[“Scale factor at natural origin”, 0.857385503731176,

SCALEUNIT[“unity”,1.0]],

·         PARAMETER[“False easting”,0,LENGTHUNIT[“metre”,1.0]],

·         PARAMETER[“False northing”,0,LENGTHUNIT[“metre”,1.0]],

 

            A6.5 Likewise, the formula for the reciprocal scale can be restated:

 

reciprocal scale  meters/pixel

 

 

A7. Tiled transverse Mercator, again

 

This section re-states the forward mapping equations for tiled transverse Mercator, for the same reasons given in the introduction to Section A6 for re-stating tiled Mercator.

 

 

            A7.1 The forward mapping equations are:

 

            where

,

n is the zoom level,

 and  are defined in Section 3.2 of NGA.SIG.0012_2.0.0_UTMUPS.

 

The constant  was found by computing .  Note that  here has a close but different value than for tiled Mercator in Section A6.  The fact that they are different is due to the ellipsoidal shape of the Earth.  The fact that they are close is due to the nearly spherical shape of the ellipsoid.

 

 

            A7.2 The EPSG operation-method-code for this is EPSG::9807 with these parameters:

 

·          is the above

·        

·         (central meridian) is a longitude whose degree value is an odd integer divisible by 3.

·         FE

·         FN

 

 

            A7.3 The Well-Known-Text formats for the above EPSG parameters are found in NGA.IP.xxxx_x.x, National System for Geospatial Intelligence (NSG) GeoPackage Encoding Standard 1.0 Implementation Interoperability Standard (DRAFT), and are not repeated here.

 

            A7.4  Likewise, the formula for the reciprocal scale can be re-stated;

 

reciprocal scale  meters/pixel

 

 

A8. Tiled polar stereographic, again

 

This section re-states the forward mapping equations for tiled polar stereographic for the same reasons given in the introduction to Section A6 for re-stating tiled Mercator.

 

            A8.1 The forward mapping equations are:

 

            For the NORTH polar stereographic projection,

           

For the SOUTH polar stereographic projection,

 

            For the both NORTH and SOUTH polar stereographic projections,

            where

                       

n is the zoom level,

 and  are defined in Section 8.1 of NGA.SIG.0012_2.0.0_UTMUPS.

 

           

            A8.2 The EPSG operation-method-code for this is EPSG::9810 with these parameters:

 

·          is the above

·         , i.e. the radian equivalent of ±90°

·         (central meridian) is a longitude whose degree value is a multiple of 90.

·         FE

·         FN

 

           

            A8.3 The Well-Known-Text formats for the above EPSG parameters are found in NGA.IP.xxxx_x.x, National System for Geospatial Intelligence (NSG) GeoPackage Encoding Standard 1.0 Implementation Interoperability Standard (DRAFT), and are not repeated here.

 

            A8.4 The constant  was found by computing , where  is a defined constant (in radians) equivalent to 59°, and f3 refers to the function defined in section 8.1 of NGA.SIG.0012_2.0.0_UTMUPS.

 

 

 

 

 


 

Table 2: Tiled Mercator zoom-levels scale sets

 

n

0

156543

156519

156448

156330

156164

155951

155691

155384

155030

154628

1

78271.5

78259.7

78224.2

78165.0

78082.1

77975.7

77845.6

77692.0

77514.8

77314.2

2

39135.8

39129.8

39112.1

39082.5

39041.1

38987.8

38922.8

38846.0

38757.4

38657.1

3

19567.9

19564.9

19556.0

19541.2

19520.5

19493.9

19461.4

19423.0

19378.7

19328.5

4

9783.94

9782.46

9778.02

9770.62

9760.27

9746.96

9730.70

9711.49

9689.35

9664.27

5

4891.97

4891.23

4889.01

4885.31

4880.13

4873.48

4865.35

4855.75

4844.68

4832.14

6

2445.98

2445.61

2444.50

2442.66

2440.07

2436.74

2432.67

2427.87

2422.34

2416.07

7

1222.99

1222.81

1222.25

1221.33

1220.03

1218.37

1216.34

1213.94

1211.17

1208.03

8

611.496

611.404

611.126

610.664

610.017

609.185

608.169

606.968

605.584

604.017

9

305.748

305.702

305.563

305.332

305.008

304.592

304.084

303.484

302.792

302.009

10

152.874

152.851

152.782

152.666

152.504

152.296

152.042

151.742

151.396

151.004

11

76.4370

76.4255

76.3908

76.3330

76.2521

76.1481

76.0211

75.8711

75.6981

75.5021

12

38.2185

38.2127

38.1954

38.1665

38.1260

38.0740

38.0105

37.9355

37.8490

37.7511

13

19.1093

19.1064

19.0977

19.0832

19.0630

19.0370

19.0053

18.9678

18.9245

18.8755

14

9.55463

9.55318

9.54885

9.54162

9.53151

9.51851

9.50263

9.48388

9.46226

9.43777

15

4.77731

4.77659

4.77442

4.77081

4.76575

4.75926

4.75132

4.74194

4.73113

4.71888

16

2.38866

2.38830

2.38721

2.38541

2.38288

2.37963

2.37566

2.37097

2.36556

2.35944

17

1.19433

1.19415

1.19361

1.19270

1.19144

1.18981

1.18783

1.18549

1.18278

1.17972

18

0.597164

0.597074

0.596803

0.596351

0.595719

0.594907

0.593915

0.592743

0.591391

0.589861

19

0.298582

0.298537

0.298401

0.298176

0.297860

0.297454

0.296957

0.296371

0.295696

0.294930

20

0.149291

0.149268

0.149201

0.149088

0.148930

0.148727

0.148479

0.148186

0.147848

0.147465

21

0.0746455

0.0746342

0.0746004

0.0745439

0.0744649

0.0743634

0.0742393

0.0740928

0.0739239

0.0737326

22

0.0373228

0.0373171

0.0373002

0.0372720

0.0372325

0.0371817

0.0371197

0.0370464

0.0369619

0.0368663

23

0.0186614

0.0186586

0.0186501

0.0186360

0.0186162

0.0185908

0.0185598

0.0185232

0.0184810

0.0184331

24

0.00933069

0.00932928

0.00932505

0.00931799

0.00930811

0.00929542

0.00927992

0.00926160

0.00924049

0.00921657

 

 

 

 

 

 

 

 

 

 

 

n

10°

11°

12°

13°

14°

15°

16°

17°

18°

19°

0

154180

153686

153144

152557

151923

151243

150517

149746

148929

148067

1

77090.2

76842.8

76572.2

76278.3

75961.4

75621.4

75258.6

74872.8

74464.4

74033.4

2

38545.1

38421.4

38286.1

38139.2

37980.7

37810.7

37629.3

37436.4

37232.2

37016.7

3

19272.5

19210.7

19143.0

19069.6

18990.4

18905.4

18814.6

18718.2

18616.1

18508.4

4

9636.27

9605.35

9571.52

9534.79

9495.18

9452.68

9407.32

9359.11

9308.06

9254.18

5

4818.14

4802.68

4785.76

4767.40

4747.59

4726.34

4703.66

4679.55

4654.03

4627.09

6

2409.07

2401.34

2392.88

2383.70

2373.79

2363.17

2351.83

2339.78

2327.01

2313.55

7

1204.53

1200.67

1196.44

1191.85

1186.90

1181.58

1175.91

1169.89

1163.51

1156.77

8

602.267

600.334

598.220

595.925

593.448

590.792

587.957

584.944

581.753

578.386

9

301.134

300.167

299.110

297.962

296.724

295.396

293.979

292.472

290.877

289.193

10

150.567

150.084

149.555

148.981

148.362

147.698

146.989

146.236

145.438

144.597

11

75.2834

75.0418

74.7775

74.4906

74.1811

73.8491

73.4947

73.1180

72.7192

72.2983

12

37.6417

37.5209

37.3888

37.2453

37.0905

36.9245

36.7473

36.5590

36.3596

36.1491

13

18.8208

18.7605

18.6944

18.6226

18.5453

18.4623

18.3737

18.2795

18.1798

18.0746

14

9.41042

9.38023

9.34719

9.31132

9.27263

9.23113

9.18683

9.13975

9.08990

9.03729

15

4.70521

4.69011

4.67359

4.65566

4.63632

4.61557

4.59342

4.56988

4.54495

4.51864

16

2.35261

2.34506

2.33680

2.32783

2.31816

2.30778

2.29671

2.28494

2.27247

2.25932

17

1.17630

1.17253

1.16840

1.16392

1.15908

1.15389

1.14835

1.14247

1.13624

1.12966

18

0.588151

0.586264

0.584199

0.581958

0.579539

0.576946

0.574177

0.571235

0.568119

0.564830

19

0.294076

0.293132

0.292100

0.290979

0.289770

0.288473

0.287089

0.285617

0.284059

0.282415

20

0.147038

0.146566

0.146050

0.145489

0.144885

0.144236

0.143544

0.142809

0.142030

0.141208

21

0.0735189

0.0732830

0.0730249

0.0727447

0.0724424

0.0721182

0.0717721

0.0714043

0.0710148

0.0706038

22

0.0367595

0.0366415

0.0365125

0.0363723

0.0362212

0.0360591

0.0358861

0.0357022

0.0355074

0.0353019

23

0.0183797

0.0183208

0.0182562

0.0181862

0.0181106

0.0180296

0.0179430

0.0178511

0.0177537

0.0176509

24

0.00918987

0.00916038

0.00912811

0.00909309

0.00905530

0.00901478

0.00897152

0.00892554

0.00887685

0.00882547

Table 2: Tiled Mercator zoom-levels scale sets

 

n

20°

21°

22°

23°

24°

25°

26°

27°

28°

29°

0

147160

146208

145212

144172

143088

141961

140791

139577

138321

137023

1

73580.0

73104.2

72606.2

72086.2

71544.2

70980.5

70395.3

69788.6

69160.7

68511.7

2

36790.0

36552.1

36303.1

36043.1

35772.1

35490.3

35197.6

34894.3

34580.3

34255.9

3

18395.0

18276.0

18151.5

18021.5

17886.1

17745.1

17598.8

17447.1

17290.2

17127.9

4

9197.50

9138.02

9075.77

9010.77

8943.03

8872.57

8799.41

8723.57

8645.09

8563.97

5

4598.75

4569.01

4537.89

4505.38

4471.51

4436.28

4399.70

4361.79

4322.54

4281.98

6

2299.37

2284.51

2268.94

2252.69

2235.76

2218.14

2199.85

2180.89

2161.27

2140.99

7

1149.69

1142.25

1134.47

1126.35

1117.88

1109.07

1099.93

1090.45

1080.64

1070.50

8

574.844

571.126

567.236

563.173

558.939

554.535

549.963

545.223

540.318

535.248

9

287.422

285.563

283.618

281.587

279.470

277.268

274.982

272.612

270.159

267.624

10

143.711

142.782

141.809

140.793

139.735

138.634

137.491

136.306

135.079

133.812

11

71.8555

71.3908

70.9045

70.3966

69.8674

69.3169

68.7454

68.1529

67.5397

66.9060

12

35.9277

35.6954

35.4522

35.1983

34.9337

34.6585

34.3727

34.0765

33.7699

33.4530

13

17.9639

17.8477

17.7261

17.5992

17.4668

17.3292

17.1863

17.0382

16.8849

16.7265

14

8.98193

8.92385

8.86306

8.79958

8.73342

8.66462

8.59317

8.51912

8.44247

8.36325

15

4.49097

4.46193

4.43153

4.39979

4.36671

4.33231

4.29659

4.25956

4.22123

4.18162

16

2.24548

2.23096

2.21577

2.19989

2.18336

2.16615

2.14829

2.12978

2.11062

2.09081

17

1.12274

1.11548

1.10788

1.09995

1.09168

1.08308

1.07415

1.06489

1.05531

1.04541

18

0.561371

0.557741

0.553941

0.549974

0.545839

0.541538

0.537073

0.532445

0.527654

0.522703

19

0.280685

0.278870

0.276971

0.274987

0.272920

0.270769

0.268537

0.266222

0.263827

0.261352

20

0.140343

0.139435

0.138485

0.137493

0.136460

0.135385

0.134268

0.133111

0.131914

0.130676

21

0.0701713

0.0697176

0.0692427

0.0687467

0.0682299

0.0676923

0.0671342

0.0665556

0.0659568

0.0653379

22

0.0350857

0.0348588

0.0346213

0.0343734

0.0341149

0.0338462

0.0335671

0.0332778

0.0329784

0.0326689

23

0.0175428

0.0174294

0.0173107

0.0171867

0.0170575

0.0169231

0.0167835

0.0166389

0.0164892

0.0163345

24

0.00877142

0.00871470

0.00865533

0.00859334

0.00852874

0.00846154

0.00839177

0.00831945

0.00824460

0.00816723

 

 

n

30°

31°

32°

33°

34°

35°

36°

37°

38°

39°

0

135684

134303

132881

131419

129916

128374

126793

125173

123514

121818

1

67841.9

67151.4

66440.5

65709.3

64958.1

64187.0

63396.3

62586.3

61757.2

60909.2

2

33921.0

33575.7

33220.2

32854.6

32479.0

32093.5

31698.2

31293.2

30878.6

30454.6

3

16960.5

16787.9

16610.1

16427.3

16239.5

16046.7

15849.1

15646.6

15439.3

15227.3

4

8480.24

8393.93

8305.06

8213.66

8119.76

8023.37

7924.54

7823.29

7719.65

7613.65

5

4240.12

4196.96

4152.53

4106.83

4059.88

4011.69

3962.27

3911.65

3859.82

3806.82

6

2120.06

2098.48

2076.27

2053.42

2029.94

2005.84

1981.14

1955.82

1929.91

1903.41

7

1060.03

1049.24

1038.13

1026.71

1014.97

1002.92

990.568

977.911

964.956

951.706

8

530.015

524.621

519.066

513.354

507.485

501.461

495.284

488.956

482.478

475.853

9

265.007

262.310

259.533

256.677

253.742

250.730

247.642

244.478

241.239

237.927

10

132.504

131.155

129.767

128.338

126.871

125.365

123.821

122.239

120.620

118.963

11

66.2519

65.5776

64.8833

64.1692

63.4356

62.6826

61.9105

61.1195

60.3098

59.4816

12

33.1259

32.7888

32.4416

32.0846

31.7178

31.3413

30.9552

30.5597

30.1549

29.7408

13

16.5630

16.3944

16.2208

16.0423

15.8589

15.6707

15.4776

15.2799

15.0774

14.8704

14

8.28148

8.19720

8.11041

8.02115

7.92945

7.83533

7.73881

7.63993

7.53872

7.43520

15

4.14074

4.09860

4.05521

4.01058

3.96472

3.91766

3.86941

3.81997

3.76936

3.71760

16

2.07037

2.04930

2.02760

2.00529

1.98236

1.95883

1.93470

1.90998

1.88468

1.85880

17

1.03519

1.02465

1.01380

1.00264

0.991181

0.979416

0.967351

0.954992

0.942340

0.929400

18

0.517593

0.512325

0.506901

0.501322

0.495591

0.489708

0.483676

0.477496

0.471170

0.464700

19

0.258796

0.256162

0.253450

0.250661

0.247795

0.244854

0.241838

0.238748

0.235585

0.232350

20

0.129398

0.128081

0.126725

0.125331

0.123898

0.122427

0.120919

0.119374

0.117793

0.116175

21

0.0646991

0.0640406

0.0633626

0.0626653

0.0619488

0.0612135

0.0604595

0.0596870

0.0588963

0.0580875

22

0.0323495

0.0320203

0.0316813

0.0313326

0.0309744

0.0306067

0.0302297

0.0298435

0.0294481

0.0290438

23

0.0161748

0.0160101

0.0158406

0.0156663

0.0154872

0.0153034

0.0151149

0.0149217

0.0147241

0.0145219

24

0.00808739

0.00800507

0.00792032

0.00783316

0.00774360

0.00765169

0.00755743

0.00746087

0.00736203

0.00726094

Table 2: Tiled Mercator zoom-levels scale sets

 

n

40°

41°

42°

43°

44°

45°

46°

47°

48°

49°

0

120085

118315

116509

114667

112790

110878

108933

106954

104942

102898

1

60042.6

59157.6

58254.4

57333.5

56395.0

55439.2

54466.4

53476.9

52471.0

51448.9

2

30021.3

29578.8

29127.2

28666.7

28197.5

27719.6

27233.2

26738.4

26235.5

25724.5

3

15010.6

14789.4

14563.6

14333.4

14098.7

13859.8

13616.6

13369.2

13117.7

12862.2

4

7505.32

7394.69

7281.81

7166.69

7049.37

6929.90

6808.30

6684.61

6558.87

6431.11

5

3752.66

3697.35

3640.90

3583.34

3524.69

3464.95

3404.15

3342.30

3279.43

3215.56

6

1876.33

1848.67

1820.45

1791.67

1762.34

1732.47

1702.07

1671.15

1639.72

1607.78

7

938.165

924.337

910.226

895.836

881.172

866.237

851.037

835.576

819.859

803.889

8

469.082

462.168

455.113

447.918

440.586

433.119

425.519

417.788

409.929

401.945

9

234.541

231.084

227.556

223.959

220.293

216.559

212.759

208.894

204.965

200.972

10

117.271

115.542

113.778

111.979

110.146

108.280

106.380

104.447

102.482

100.486

11

58.6353

57.7710

56.8891

55.9897

55.0732

54.1398

53.1898

52.2235

51.2412

50.2431

12

29.3177

28.8855

28.4446

27.9949

27.5366

27.0699

26.5949

26.1118

25.6206

25.1215

13

14.6588

14.4428

14.2223

13.9974

13.7683

13.5350

13.2975

13.0559

12.8103

12.5608

14

7.32941

7.22138

7.11114

6.99872

6.88415

6.76748

6.64873

6.52794

6.40515

6.28039

15

3.66471

3.61069

3.55557

3.49936

3.44208

3.38374

3.32436

3.26397

3.20257

3.14019

16

1.83235

1.80535

1.77778

1.74968

1.72104

1.69187

1.66218

1.63198

1.60129

1.57010

17

0.916177

0.902673

0.888892

0.874840

0.860519

0.845935

0.831091

0.815992

0.800643

0.785048

18

0.458088

0.451336

0.444446

0.437420

0.430260

0.422967

0.415546

0.407996

0.400322

0.392524

19

0.229044

0.225668

0.222223

0.218710

0.215130

0.211484

0.207773

0.203998

0.200161

0.196262

20

0.114522

0.112834

0.111112

0.109355

0.107565

0.105742

0.103886

0.101999

0.100080

0.0981310

21

0.0572610

0.0564170

0.0555558

0.0546775

0.0537824

0.0528709

0.0519432

0.0509995

0.0500402

0.0490655

22

0.0286305

0.0282085

0.0277779

0.0273387

0.0268912

0.0264355

0.0259716

0.0254998

0.0250201

0.0245328

23

0.0143153

0.0141043

0.0138889

0.0136694

0.0134456

0.0132177

0.0129858

0.0127499

0.0125100

0.0122664

24

0.00715763

0.00705213

0.00694447

0.00683468

0.00672281

0.00660887

0.00649290

0.00637494

0.00625502

0.00613319

n

50°

51°

52°

53°

54°

55°

56°

57°

58°

59°

0

100822

98715.5

96578.5

94411.7

92215.9

89991.7

87739.8

85460.9

83155.6

80824.6

1

50411.1

49357.7

48289.2

47205.9

46108.0

44995.9

43869.9

42730.4

41577.8

40412.3

2

25205.5

24678.9

24144.6

23602.9

23054.0

22497.9

21935.0

21365.2

20788.9

20206.2

3

12602.8

12339.4

12072.3

11801.5

11527.0

11249.0

10967.5

10682.6

10394.4

10103.1

4

6301.38

6169.72

6036.15

5900.73

5763.50

5624.48

5483.74

5341.31

5197.22

5051.54

5

3150.69

3084.86

3018.08

2950.37

2881.75

2812.24

2741.87

2670.65

2598.61

2525.77

6

1575.35

1542.43

1509.04

1475.18

1440.87

1406.12

1370.93

1335.33

1299.31

1262.88

7

787.673

771.215

754.519

737.592

720.437

703.061

685.467

667.663

649.653

631.442

8

393.837

385.607

377.260

368.796

360.218

351.530

342.734

333.832

324.827

315.721

9

196.918

192.804

188.630

184.398

180.109

175.765

171.367

166.916

162.413

157.861

10

98.4591

96.4018

94.3149

92.1990

90.0546

87.8826

85.6834

83.4579

81.2066

78.9303

11

49.2296

48.2009

47.1575

46.0995

45.0273

43.9413

42.8417

41.7289

40.6033

39.4652

12

24.6148

24.1005

23.5787

23.0497

22.5137

21.9706

21.4209

20.8645

20.3017

19.7326

13

12.3074

12.0502

11.7894

11.5249

11.2568

10.9853

10.7104

10.4322

10.1508

9.86629

14

6.15370

6.02512

5.89468

5.76243

5.62841

5.49266

5.35521

5.21612

5.07541

4.93314

15

3.07685

3.01256

2.94734

2.88122

2.81421

2.74633

2.67761

2.60806

2.53771

2.46657

16

1.53842

1.50628

1.47367

1.44061

1.40710

1.37317

1.33880

1.30403

1.26885

1.23329

17

0.769212

0.753139

0.736835

0.720304

0.703552

0.686583

0.669402

0.652015

0.634427

0.616643

18

0.384606

0.376570

0.368418

0.360152

0.351776

0.343291

0.334701

0.326007

0.317213

0.308322

19

0.192303

0.188285

0.184209

0.180076

0.175888

0.171646

0.167350

0.163004

0.158607

0.154161

20

0.0961515

0.0941424

0.0921044

0.0900380

0.0879440

0.0858228

0.0836752

0.0815019

0.0793033

0.0770804

21

0.0480757

0.0470712

0.0460522

0.0450190

0.0439720

0.0429114

0.0418376

0.0407509

0.0396517

0.0385402

22

0.0240379

0.0235356

0.0230261

0.0225095

0.0219860

0.0214557

0.0209188

0.0203755

0.0198258

0.0192701

23

0.0120189

0.0117678

0.0115130

0.0112548

0.0109930

0.0107279

0.0104594

0.0101877

0.00991292

0.00963505

24

0.00600947

0.00588390

0.00575652

0.00562738

0.00549650

0.00536393

0.00522970

0.00509387

0.00495646

0.00481752

Table 2: Tiled Mercator zoom-levels scale sets

 

n

60°

61°

62°

63°

64°

65°

66°

67°

68°

69°

0

78468.8

76088.6

73685.0

71258.7

68810.3

66340.6

63850.4

61340.5

58811.5

56264.4

1

39234.4

38044.3

36842.5

35629.3

34405.1

33170.3

31925.2

30670.2

29405.8

28132.2

2

19617.2

19022.2

18421.3

17814.7

17202.6

16585.1

15962.6

15335.1

14702.9

14066.1

3

9808.59

9511.08

9210.63

8907.33

8601.28

8292.57

7981.30

7667.56

7351.44

7033.05

4

4904.30

4755.54

4605.31

4453.67

4300.64

4146.29

3990.65

3833.78

3675.72

3516.52

5

2452.15

2377.77

2302.66

2226.83

2150.32

2073.14

1995.33

1916.89

1837.86

1758.26

6

1226.07

1188.89

1151.33

1113.42

1075.16

1036.57

997.663

958.445

918.930

879.131

7

613.037

594.443

575.664

556.708

537.580

518.286

498.831

479.222

459.465

439.566

8

306.519

297.221

287.832

278.354

268.790

259.143

249.416

239.611

229.733

219.783

9

153.259

148.611

143.916

139.177

134.395

129.571

124.708

119.806

114.866

109.891

10

76.6296

74.3053

71.9580

69.5885

67.1975

64.7857

62.3539

59.9028

57.4331

54.9457

11

38.3148

37.1527

35.9790

34.7943

33.5988

32.3929

31.1770

29.9514

28.7166

27.4728

12

19.1574

18.5763

17.9895

17.3971

16.7994

16.1964

15.5885

14.9757

14.3583

13.7364

13

9.57871

9.28816

8.99475

8.69857

8.39969

8.09822

7.79424

7.48785

7.17914

6.86821

14

4.78935

4.64408

4.49738

4.34928

4.19985

4.04911

3.89712

3.74392

3.58957

3.43411

15

2.39468

2.32204

2.24869

2.17464

2.09992

2.02455

1.94856

1.87196

1.79479

1.71705

16

1.19734

1.16102

1.12434

1.08732

1.04996

1.01228

0.974280

0.935981

0.897393

0.858526

17

0.598669

0.580510

0.562172

0.543660

0.524981

0.506139

0.487140

0.467991

0.448696

0.429263

18

0.299335

0.290255

0.281086

0.271830

0.262490

0.253069

0.243570

0.233995

0.224348

0.214632

19

0.149667

0.145128

0.140543

0.135915

0.131245

0.126535

0.121785

0.116998

0.112174

0.107316

20

0.0748336

0.0725638

0.0702715

0.0679576

0.0656226

0.0632673

0.0608925

0.0584988

0.0560870

0.0536579

21

0.0374168

0.0362819

0.0351358

0.0339788

0.0328113

0.0316337

0.0304462

0.0292494

0.0280435

0.0268290

22

0.0187084

0.0181409

0.0175679

0.0169894

0.0164056

0.0158168

0.0152231

0.0146247

0.0140218

0.0134145

23

0.00935420

0.00907047

0.00878394

0.00849469

0.00820282

0.00790841

0.00761156

0.00731235

0.00701088

0.00670724

24

0.00467710

0.00453524

0.00439197

0.00424735

0.00410141

0.00395421

0.00380578

0.00365618

0.00350544

0.00335362

n

70°

71°

72°

73°

74°

75°

76°

77°

78°

79°

0

53699.8

51118.6

48521.6

45909.5

43283.2

40643.4

37991.1

35327.0

32651.9

29966.6

1

26849.9

25559.3

24260.8

22954.8

21641.6

20321.7

18995.5

17663.5

16325.9

14983.3

2

13425.0

12779.7

12130.4

11477.4

10820.8

10160.9

9497.77

8831.74

8162.97

7491.66

3

6712.48

6389.83

6065.20

5738.69

5410.40

5080.43

4748.89

4415.87

4081.48

3745.83

4

3356.24

3194.91

3032.60

2869.34

2705.20

2540.22

2374.44

2207.94

2040.74

1872.91

5

1678.12

1597.46

1516.30

1434.67

1352.60

1270.11

1187.22

1103.97

1020.37

936.457

6

839.060

798.728

758.150

717.336

676.300

635.054

593.611

551.984

510.185

468.229

7

419.530

399.364

379.075

358.668

338.150

317.527

296.805

275.992

255.093

234.114

8

209.765

199.682

189.537

179.334

169.075

158.763

148.403

137.996

127.546

117.057

9

104.882

99.8411

94.7687

89.6670

84.5375

79.3817

74.2014

68.9980

63.7732

58.5286

10

52.4412

49.9205

47.3844

44.8335

42.2687

39.6909

37.1007

34.4990

31.8866

29.2643

11

26.2206

24.9603

23.6922

22.4167

21.1344

19.8454

18.5503

17.2495

15.9433

14.6321

12

13.1103

12.4801

11.8461

11.2084

10.5672

9.92272

9.27517

8.62475

7.97165

7.31607

13

6.55515

6.24007

5.92304

5.60419

5.28359

4.96136

4.63759

4.31237

3.98582

3.65804

14

3.27758

3.12003

2.96152

2.80209

2.64180

2.48068

2.31879

2.15619

1.99291

1.82902

15

1.63879

1.56002

1.48076

1.40105

1.32090

1.24034

1.15940

1.07809

0.996456

0.914509

16

0.819394

0.780008

0.740381

0.700523

0.660449

0.620170

0.579698

0.539047

0.498228

0.457254

17

0.409697

0.390004

0.370190

0.350262

0.330224

0.310085

0.289849

0.269523

0.249114

0.228627

18

0.204849

0.195002

0.185095

0.175131

0.165112

0.155042

0.144925

0.134762

0.124557

0.114314

19

0.102424

0.0975010

0.0925476

0.0875654

0.0825561

0.0775212

0.0724623

0.0673808

0.0622785

0.0571568

20

0.0512121

0.0487505

0.0462738

0.0437827

0.0412781

0.0387606

0.0362311

0.0336904

0.0311392

0.0285784

21

0.0256061

0.0243753

0.0231369

0.0218914

0.0206390

0.0193803

0.0181156

0.0168452

0.0155696

0.0142892

22

0.0128030

0.0121876

0.0115684

0.0109457

0.0103195

0.00969015

0.00905778

0.00842260

0.00778481

0.00714460

23

0.00640152

0.00609381

0.00578422

0.00547284

0.00515976

0.00484508

0.00452889

0.00421130

0.00389241

0.00357230

24

0.00320076

0.00304691

0.00289211

0.00273642

0.00257988

0.00242254

0.00226445

0.00210565

0.00194620

0.00178615

Table 2: Tiled Mercator zoom-levels scale sets

 

n

80°

81°

82°

83°

84°

85°

0

27272.1

24569.1

21858.4

19141.0

16417.6

13689.2

1

13636.0

12284.5

10929.2

9570.51

8208.82

6844.59

2

6818.02

6142.27

5464.61

4785.25

4104.41

3422.29

3

3409.01

3071.14

2732.31

2392.63

2052.21

1711.15

4

1704.51

1535.57

1366.15

1196.31

1026.10

855.573

5

852.253

767.784

683.076

598.157

513.051

427.787

6

426.126

383.892

341.538

299.078

256.526

213.893

7

213.063

191.946

170.769

149.539

128.263

106.947

8

106.532

95.9730

85.3846

74.7696

64.1314

53.4733

9

53.2658

47.9865

42.6923

37.3848

32.0657

26.7367

10

26.6329

23.9932

21.3461

18.6924

16.0329

13.3683

11

13.3164

11.9966

10.6731

9.34620

8.01643

6.68417

12

6.65822

5.99831

5.33653

4.67310

4.00821

3.34208

13

3.32911

2.99916

2.66827

2.33655

2.00411

1.67104

14

1.66456

1.49958

1.33413

1.16828

1.00205

0.835521

15

0.832278

0.749789

0.667067

0.584138

0.501027

0.417760

16

0.416139

0.374894

0.333533

0.292069

0.250513

0.208880

17

0.208070

0.187447

0.166767

0.146034

0.125257

0.104440

18

0.104035

0.0937236

0.0833833

0.0730172

0.0626283

0.0522200

19

0.0520174

0.0468618

0.0416917

0.0365086

0.0313142

0.0261100

20

0.0260087

0.0234309

0.0208458

0.0182543

0.0156571

0.0130550

21

0.0130043

0.0117155

0.0104229

0.00912715

0.00782854

0.00652751

22

0.00650217

0.00585773

0.00521146

0.00456357

0.00391427

0.00326375

23

0.00325109

0.00292886

0.00260573

0.00228179

0.00195714

0.00163188

24

0.00162554

0.00146443

0.00130286

0.00114089

0.000978568

0.000815938

 


 

Table 3: Tiled transverse Mercator zoom-levels scale sets

Longitude = Central Meridian

n

10°

15°

20°

25°

30°

35°

40°

0

156281

156281

156281

156281

156281

156281

156281

156281

156281

1

78140.4

78140.4

78140.4

78140.4

78140.4

78140.4

78140.4

78140.4

78140.4

2

39070.2

39070.2

39070.2

39070.2

39070.2

39070.2

39070.2

39070.2

39070.2

3

19535.1

19535.1

19535.1

19535.1

19535.1

19535.1

19535.1

19535.1

19535.1

4

9767.54

9767.54

9767.54

9767.54

9767.54

9767.54

9767.54

9767.54

9767.54

5

4883.77

4883.77

4883.77

4883.77

4883.77

4883.77

4883.77

4883.77

4883.77

6

2441.89

2441.89

2441.89

2441.89

2441.89

2441.89

2441.89

2441.89

2441.89

7

1220.94

1220.94

1220.94

1220.94

1220.94

1220.94

1220.94

1220.94

1220.94

8

610.472

610.472

610.472

610.472

610.472

610.472

610.472

610.472

610.472

9

305.236

305.236

305.236

305.236

305.236

305.236

305.236

305.236

305.236

10

152.618

152.618

152.618

152.618

152.618

152.618

152.618

152.618

152.618

11

76.3089

76.3089

76.3089

76.3089

76.3089

76.3089

76.3089

76.3089

76.3089

12

38.1545

38.1545

38.1545

38.1545

38.1545

38.1545

38.1545

38.1545

38.1545

13

19.0772

19.0772

19.0772

19.0772

19.0772

19.0772

19.0772

19.0772

19.0772

14

9.53862

9.53862

9.53862

9.53862

9.53862

9.53862

9.53862

9.53862

9.53862

15

4.76931

4.76931

4.76931

4.76931

4.76931

4.76931

4.76931

4.76931

4.76931

16

2.38465

2.38465

2.38465

2.38465

2.38465

2.38465

2.38465

2.38465

2.38465

17

1.19233

1.19233

1.19233

1.19233

1.19233

1.19233

1.19233

1.19233

1.19233

18

0.596164

0.596164

0.596164

0.596164

0.596164

0.596164

0.596164

0.596164

0.596164

19

0.298082

0.298082

0.298082

0.298082

0.298082

0.298082

0.298082

0.298082

0.298082

20

0.149041

0.149041

0.149041

0.149041

0.149041

0.149041

0.149041

0.149041

0.149041

21

0.0745205

0.0745205

0.0745205

0.0745205

0.0745205

0.0745205

0.0745205

0.0745205

0.0745205

22

0.0372602

0.0372602

0.0372602

0.0372602

0.0372602

0.0372602

0.0372602

0.0372602

0.0372602

23

0.0186301

0.0186301

0.0186301

0.0186301

0.0186301

0.0186301

0.0186301

0.0186301

0.0186301

24

0.00931506

0.00931506

0.00931506

0.00931506

0.00931506

0.00931506

0.00931506

0.00931506

0.00931506

Longitude = Central Meridian

n

45°

50°

55°

60°

65°

70°

75°

80°

85°

0

156281

156281

156281

156281

156281

156281

156281

156281

156281

1

78140.4

78140.4

78140.4

78140.4

78140.4

78140.4

78140.4

78140.4

78140.4

2

39070.2

39070.2

39070.2

39070.2

39070.2

39070.2

39070.2

39070.2

39070.2

3

19535.1

19535.1

19535.1

19535.1

19535.1

19535.1

19535.1

19535.1

19535.1

4

9767.54

9767.54

9767.54

9767.54

9767.54

9767.54

9767.54

9767.54

9767.54

5

4883.77

4883.77

4883.77

4883.77

4883.77

4883.77

4883.77

4883.77

4883.77

6

2441.89

2441.89

2441.89

2441.89

2441.89

2441.89

2441.89

2441.89

2441.89

7

1220.94

1220.94

1220.94

1220.94

1220.94

1220.94

1220.94

1220.94

1220.94

8

610.472

610.472

610.472

610.472

610.472

610.472

610.472

610.472

610.472

9

305.236

305.236

305.236

305.236

305.236

305.236

305.236

305.236

305.236

10

152.618

152.618

152.618

152.618

152.618

152.618

152.618

152.618

152.618

11

76.3089

76.3089

76.3089

76.3089

76.3089

76.3089

76.3089

76.3089

76.3089

12

38.1545

38.1545

38.1545

38.1545

38.1545

38.1545

38.1545

38.1545

38.1545

13

19.0772

19.0772

19.0772

19.0772

19.0772

19.0772

19.0772

19.0772

19.0772

14

9.53862

9.53862

9.53862

9.53862

9.53862

9.53862

9.53862

9.53862

9.53862

15

4.76931

4.76931

4.76931

4.76931

4.76931

4.76931

4.76931

4.76931

4.76931

16

2.38465

2.38465

2.38465

2.38465

2.38465

2.38465

2.38465

2.38465

2.38465

17

1.19233

1.19233

1.19233

1.19233

1.19233

1.19233

1.19233

1.19233

1.19233

18

0.596164

0.596164

0.596164

0.596164

0.596164

0.596164

0.596164

0.596164

0.596164

19

0.298082

0.298082

0.298082

0.298082

0.298082

0.298082

0.298082

0.298082

0.298082

20

0.149041

0.149041

0.149041

0.149041

0.149041

0.149041

0.149041

0.149041

0.149041

21

0.0745205

0.0745205

0.0745205

0.0745205

0.0745205

0.0745205

0.0745205

0.0745205

0.0745205

22

0.0372602

0.0372602

0.0372602

0.0372602

0.0372602

0.0372602

0.0372602

0.0372602

0.0372602

23

0.0186301

0.0186301

0.0186301

0.0186301

0.0186301

0.0186301

0.0186301

0.0186301

0.0186301

24

0.00931506

0.00931506

0.00931506

0.00931506

0.00931506

0.00931506

0.00931506

0.00931506

0.00931506

Table 3: Tiled transverse Mercator zoom-levels scale sets

Longitude = Central Meridian + 1°

n

10°

15°

20°

25°

30°

35°

40°

0

156257

156257

156257

156258

156260

156261

156263

156265

156267

1

78128.4

78128.5

78128.7

78129.2

78129.8

78130.5

78131.4

78132.3

78133.3

2

39064.2

39064.2

39064.4

39064.6

39064.9

39065.3

39065.7

39066.2

39066.7

3

19532.1

19532.1

19532.2

19532.3

19532.4

19532.6

19532.8

19533.1

19533.3

4

9766.05

9766.06

9766.09

9766.15

9766.22

9766.32

9766.42

9766.54

9766.67

5

4883.02

4883.03

4883.05

4883.07

4883.11

4883.16

4883.21

4883.27

4883.33

6

2441.51

2441.51

2441.52

2441.54

2441.56

2441.58

2441.61

2441.64

2441.67

7

1220.76

1220.76

1220.76

1220.77

1220.78

1220.79

1220.80

1220.82

1220.83

8

610.378

610.379

610.381

610.384

610.389

610.395

610.401

610.409

610.417

9

305.189

305.189

305.190

305.192

305.194

305.197

305.201

305.204

305.208

10

152.594

152.595

152.595

152.596

152.597

152.599

152.600

152.602

152.604

11

76.2972

76.2973

76.2976

76.2980

76.2986

76.2993

76.3002

76.3011

76.3021

12

38.1486

38.1487

38.1488

38.1490

38.1493

38.1497

38.1501

38.1506

38.1510

13

19.0743

19.0743

19.0744

19.0745

19.0747

19.0748

19.0750

19.0753

19.0755

14

9.53716

9.53717

9.53720

9.53725

9.53733

9.53742

9.53752

9.53764

9.53776

15

4.76858

4.76858

4.76860

4.76863

4.76866

4.76871

4.76876

4.76882

4.76888

16

2.38429

2.38429

2.38430

2.38431

2.38433

2.38435

2.38438

2.38441

2.38444

17

1.19214

1.19215

1.19215

1.19216

1.19217

1.19218

1.19219

1.19220

1.19222

18

0.596072

0.596073

0.596075

0.596078

0.596083

0.596089

0.596095

0.596102

0.596110

19

0.298036

0.298036

0.298037

0.298039

0.298041

0.298044

0.298048

0.298051

0.298055

20

0.149018

0.149018

0.149019

0.149020

0.149021

0.149022

0.149024

0.149026

0.149028

21

0.0745090

0.0745091

0.0745094

0.0745098

0.0745104

0.0745111

0.0745119

0.0745128

0.0745138

22

0.0372545

0.0372546

0.0372547

0.0372549

0.0372552

0.0372555

0.0372559

0.0372564

0.0372569

23

0.0186273

0.0186273

0.0186273

0.0186274

0.0186276

0.0186278

0.0186280

0.0186282

0.0186284

24

0.00931363

0.00931364

0.00931367

0.00931372

0.00931380

0.00931388

0.00931399

0.00931410

0.00931422

Longitude = Central Meridian + 1°

n

45°

50°

55°

60°

65°

70°

75°

80°

85°

0

156269

156271

156273

156275

156276

156278

156279

156280

156281

1

78134.4

78135.4

78136.4

78137.4

78138.2

78139.0

78139.6

78140.0

78140.3

2

39067.2

39067.7

39068.2

39068.7

39069.1

39069.5

39069.8

39070.0

39070.1

3

19533.6

19533.9

19534.1

19534.3

19534.6

19534.7

19534.9

19535.0

19535.1

4

9766.80

9766.93

9767.05

9767.17

9767.28

9767.37

9767.44

9767.50

9767.53

5

4883.40

4883.46

4883.53

4883.59

4883.64

4883.69

4883.72

4883.75

4883.77

6

2441.70

2441.73

2441.76

2441.79

2441.82

2441.84

2441.86

2441.87

2441.88

7

1220.85

1220.87

1220.88

1220.90

1220.91

1220.92

1220.93

1220.94

1220.94

8

610.425

610.433

610.441

610.448

610.455

610.461

610.465

610.469

610.471

9

305.212

305.217

305.220

305.224

305.227

305.230

305.233

305.234

305.235

10

152.606

152.608

152.610

152.612

152.614

152.615

152.616

152.617

152.618

11

76.3031

76.3041

76.3051

76.3060

76.3069

76.3076

76.3082

76.3086

76.3089

12

38.1516

38.1521

38.1526

38.1530

38.1534

38.1538

38.1541

38.1543

38.1544

13

19.0758

19.0760

19.0763

19.0765

19.0767

19.0769

19.0770

19.0771

19.0772

14

9.53789

9.53802

9.53814

9.53825

9.53836

9.53845

9.53852

9.53857

9.53861

15

4.76894

4.76901

4.76907

4.76913

4.76918

4.76922

4.76926

4.76929

4.76930

16

2.38447

2.38450

2.38453

2.38456

2.38459

2.38461

2.38463

2.38464

2.38465

17

1.19224

1.19225

1.19227

1.19228

1.19229

1.19231

1.19232

1.19232

1.19233

18

0.596118

0.596126

0.596134

0.596141

0.596147

0.596153

0.596158

0.596161

0.596163

19

0.298059

0.298063

0.298067

0.298070

0.298074

0.298076

0.298079

0.298080

0.298081

20

0.149030

0.149031

0.149033

0.149035

0.149037

0.149038

0.149039

0.149040

0.149041

21

0.0745148

0.0745157

0.0745167

0.0745176

0.0745184

0.0745191

0.0745197

0.0745201

0.0745204

22

0.0372574

0.0372579

0.0372584

0.0372588

0.0372592

0.0372596

0.0372598

0.0372601

0.0372602

23

0.0186287

0.0186289

0.0186292

0.0186294

0.0186296

0.0186298

0.0186299

0.0186300

0.0186301

24

0.00931434

0.00931447

0.00931459

0.00931470

0.00931480

0.00931489

0.00931496

0.00931501

0.00931505

Table 3: Tiled transverse Mercator zoom-levels scale sets

Longitude = Central Meridian + 2°

n

10°

15°

20°

25°

30°

35°

40°

0

156185

156186

156188

156191

156196

156202

156209

156217

156225

1

78092.4

78092.8

78093.9

78095.7

78098.1

78101.0

78104.5

78108.3

78112.3

2

39046.2

39046.4

39046.9

39047.8

39049.0

39050.5

39052.2

39054.1

39056.2

3

19523.1

19523.2

19523.5

19523.9

19524.5

19525.3

19526.1

19527.1

19528.1

4

9761.55

9761.60

9761.74

9761.96

9762.26

9762.63

9763.06

9763.53

9764.04

5

4880.78

4880.80

4880.87

4880.98

4881.13

4881.32

4881.53

4881.77

4882.02

6

2440.39

2440.40

2440.43

2440.49

2440.56

2440.66

2440.76

2440.88

2441.01

7

1220.19

1220.20

1220.22

1220.24

1220.28

1220.33

1220.38

1220.44

1220.50

8

610.097

610.100

610.109

610.122

610.141

610.164

610.191

610.221

610.252

9

305.049

305.050

305.054

305.061

305.071

305.082

305.096

305.110

305.126

10

152.524

152.525

152.527

152.531

152.535

152.541

152.548

152.555

152.563

11

76.2621

76.2625

76.2636

76.2653

76.2677

76.2706

76.2739

76.2776

76.2816

12

38.1311

38.1313

38.1318

38.1326

38.1338

38.1353

38.1370

38.1388

38.1408

13

19.0655

19.0656

19.0659

19.0663

19.0669

19.0676

19.0685

19.0694

19.0704

14

9.53277

9.53281

9.53295

9.53316

9.53346

9.53382

9.53424

9.53470

9.53519

15

4.76638

4.76641

4.76647

4.76658

4.76673

4.76691

4.76712

4.76735

4.76760

16

2.38319

2.38320

2.38324

2.38329

2.38336

2.38345

2.38356

2.38368

2.38380

17

1.19160

1.19160

1.19162

1.19165

1.19168

1.19173

1.19178

1.19184

1.19190

18

0.595798

0.595801

0.595809

0.595823

0.595841

0.595864

0.595890

0.595919

0.595950

19

0.297899

0.297900

0.297905

0.297911

0.297921

0.297932

0.297945

0.297959

0.297975

20

0.148949

0.148950

0.148952

0.148956

0.148960

0.148966

0.148972

0.148980

0.148987

21

0.0744747

0.0744751

0.0744761

0.0744778

0.0744801

0.0744830

0.0744862

0.0744899

0.0744937

22

0.0372374

0.0372375

0.0372381

0.0372389

0.0372401

0.0372415

0.0372431

0.0372449

0.0372469

23

0.0186187

0.0186188

0.0186190

0.0186195

0.0186200

0.0186207

0.0186216

0.0186225

0.0186234

24

0.00930934

0.00930939

0.00930952

0.00930973

0.00931002

0.00931037

0.00931078

0.00931123

0.00931171

Longitude = Central Meridian + 2°

n

45°

50°

55°

60°

65°

70°

75°

80°

85°

0

156233

156241

156249

156257

156264

156270

156274

156278

156280

1

78116.5

78120.6

78124.7

78128.4

78131.8

78134.8

78137.2

78138.9

78140.0

2

39058.2

39060.3

39062.3

39064.2

39065.9

39067.4

39068.6

39069.5

39070.0

3

19529.1

19530.2

19531.2

19532.1

19533.0

19533.7

19534.3

19534.7

19535.0

4

9764.56

9765.08

9765.58

9766.05

9766.48

9766.85

9767.15

9767.37

9767.50

5

4882.28

4882.54

4882.79

4883.03

4883.24

4883.42

4883.57

4883.68

4883.75

6

2441.14

2441.27

2441.40

2441.51

2441.62

2441.71

2441.79

2441.84

2441.87

7

1220.57

1220.63

1220.70

1220.76

1220.81

1220.86

1220.89

1220.92

1220.94

8

610.285

610.317

610.349

610.378

610.405

610.428

610.447

610.460

610.469

9

305.143

305.159

305.174

305.189

305.203

305.214

305.223

305.230

305.234

10

152.571

152.579

152.587

152.595

152.601

152.607

152.612

152.615

152.617

11

76.2856

76.2897

76.2936

76.2973

76.3006

76.3035

76.3058

76.3075

76.3086

12

38.1428

38.1448

38.1468

38.1487

38.1503

38.1518

38.1529

38.1538

38.1543

13

19.0714

19.0724

19.0734

19.0743

19.0752

19.0759

19.0765

19.0769

19.0771

14

9.53570

9.53621

9.53670

9.53716

9.53758

9.53794

9.53823

9.53844

9.53857

15

4.76785

4.76811

4.76835

4.76858

4.76879

4.76897

4.76911

4.76922

4.76929

16

2.38393

2.38405

2.38418

2.38429

2.38439

2.38448

2.38456

2.38461

2.38464

17

1.19196

1.19203

1.19209

1.19215

1.19220

1.19224

1.19228

1.19231

1.19232

18

0.595981

0.596013

0.596044

0.596073

0.596099

0.596121

0.596139

0.596153

0.596161

19

0.297991

0.298007

0.298022

0.298036

0.298049

0.298061

0.298070

0.298076

0.298080

20

0.148995

0.149003

0.149011

0.149018

0.149025

0.149030

0.149035

0.149038

0.149040

21

0.0744977

0.0745016

0.0745055

0.0745091

0.0745123

0.0745151

0.0745174

0.0745191

0.0745201

22

0.0372488

0.0372508

0.0372527

0.0372545

0.0372562

0.0372576

0.0372587

0.0372595

0.0372601

23

0.0186244

0.0186254

0.0186264

0.0186273

0.0186281

0.0186288

0.0186294

0.0186298

0.0186300

24

0.00931221

0.00931271

0.00931319

0.00931364

0.00931404

0.00931439

0.00931468

0.00931489

0.00931501

Table 3: Tiled transverse Mercator zoom-levels scale sets

Longitude = Central Meridian + 3°

n

10°

15°

20°

25°

30°

35°

40°

0

156065

156067

156072

156080

156090

156104

156119

156136

156155

1

78032.5

78033.4

78035.8

78039.8

78045.2

78051.9

78059.6

78068.2

78077.3

2

39016.3

39016.7

39017.9

39019.9

39022.6

39026.0

39029.8

39034.1

39038.6

3

19508.1

19508.3

19509.0

19510.0

19511.3

19513.0

19514.9

19517.0

19519.3

4

9754.07

9754.17

9754.48

9754.98

9755.66

9756.49

9757.46

9758.52

9759.66

5

4877.03

4877.09

4877.24

4877.49

4877.83

4878.24

4878.73

4879.26

4879.83

6

2438.52

2438.54

2438.62

2438.74

2438.91

2439.12

2439.36

2439.63

2439.92

7

1219.26

1219.27

1219.31

1219.37

1219.46

1219.56

1219.68

1219.82

1219.96

8

609.629

609.636

609.655

609.686

609.728

609.781

609.841

609.908

609.979

9

304.815

304.818

304.827

304.843

304.864

304.890

304.921

304.954

304.989

10

152.407

152.409

152.414

152.422

152.432

152.445

152.460

152.477

152.495

11

76.2037

76.2045

76.2069

76.2108

76.2161

76.2226

76.2301

76.2385

76.2473

12

38.1018

38.1022

38.1034

38.1054

38.1080

38.1113

38.1151

38.1192

38.1237

13

19.0509

19.0511

19.0517

19.0527

19.0540

19.0556

19.0575

19.0596

19.0618

14

9.52546

9.52556

9.52586

9.52635

9.52701

9.52782

9.52877

9.52981

9.53092

15

4.76273

4.76278

4.76293

4.76317

4.76350

4.76391

4.76438

4.76490

4.76546

16

2.38136

2.38139

2.38146

2.38159

2.38175

2.38196

2.38219

2.38245

2.38273

17

1.19068

1.19069

1.19073

1.19079

1.19088

1.19098

1.19110

1.19123

1.19136

18

0.595341

0.595347

0.595366

0.595397

0.595438

0.595489

0.595548

0.595613

0.595682

19

0.297671

0.297674

0.297683

0.297698

0.297719

0.297744

0.297774

0.297807

0.297841

20

0.148835

0.148837

0.148842

0.148849

0.148859

0.148872

0.148887

0.148903

0.148921

21

0.0744176

0.0744184

0.0744208

0.0744246

0.0744297

0.0744361

0.0744435

0.0744516

0.0744603

22

0.0372088

0.0372092

0.0372104

0.0372123

0.0372149

0.0372181

0.0372217

0.0372258

0.0372302

23

0.0186044

0.0186046

0.0186052

0.0186061

0.0186074

0.0186090

0.0186109

0.0186129

0.0186151

24

0.00930220

0.00930230

0.00930259

0.00930307

0.00930372

0.00930451

0.00930544

0.00930645

0.00930754

Longitude = Central Meridian + 3°

n

45°

50°

55°

60°

65°

70°

75°

80°

85°

0

156173

156192

156210

156227

156242

156256

156266

156274

156279

1

78086.7

78096.0

78105.1

78113.6

78121.2

78127.8

78133.2

78137.1

78139.5

2

39043.3

39048.0

39052.5

39056.8

39060.6

39063.9

39066.6

39068.6

39069.8

3

19521.7

19524.0

19526.3

19528.4

19530.3

19532.0

19533.3

19534.3

19534.9

4

9760.83

9762.00

9763.13

9764.19

9765.15

9765.98

9766.65

9767.14

9767.44

5

4880.42

4881.00

4881.57

4882.10

4882.58

4882.99

4883.32

4883.57

4883.72

6

2440.21

2440.50

2440.78

2441.05

2441.29

2441.49

2441.66

2441.79

2441.86

7

1220.10

1220.25

1220.39

1220.52

1220.64

1220.75

1220.83

1220.89

1220.93

8

610.052

610.125

610.196

610.262

610.322

610.374

610.416

610.446

610.465

9

305.026

305.063

305.098

305.131

305.161

305.187

305.208

305.223

305.233

10

152.513

152.531

152.549

152.566

152.581

152.593

152.604

152.612

152.616

11

76.2565

76.2656

76.2745

76.2828

76.2903

76.2967

76.3019

76.3058

76.3081

12

38.1282

38.1328

38.1372

38.1414

38.1451

38.1484

38.1510

38.1529

38.1541

13

19.0641

19.0664

19.0686

19.0707

19.0726

19.0742

19.0755

19.0764

19.0770

14

9.53206

9.53320

9.53431

9.53535

9.53628

9.53709

9.53774

9.53822

9.53852

15

4.76603

4.76660

4.76715

4.76767

4.76814

4.76854

4.76887

4.76911

4.76926

16

2.38302

2.38330

2.38358

2.38384

2.38407

2.38427

2.38444

2.38456

2.38463

17

1.19151

1.19165

1.19179

1.19192

1.19204

1.19214

1.19222

1.19228

1.19231

18

0.595754

0.595825

0.595894

0.595959

0.596018

0.596068

0.596109

0.596139

0.596157

19

0.297877

0.297913

0.297947

0.297980

0.298009

0.298034

0.298054

0.298069

0.298079

20

0.148938

0.148956

0.148974

0.148990

0.149004

0.149017

0.149027

0.149035

0.149039

21

0.0744692

0.0744782

0.0744868

0.0744949

0.0745022

0.0745085

0.0745136

0.0745174

0.0745197

22

0.0372346

0.0372391

0.0372434

0.0372474

0.0372511

0.0372543

0.0372568

0.0372587

0.0372598

23

0.0186173

0.0186195

0.0186217

0.0186237

0.0186255

0.0186271

0.0186284

0.0186293

0.0186299

24

0.00930865

0.00930977

0.00931085

0.00931186

0.00931277

0.00931356

0.00931420

0.00931467

0.00931496

Table 3: Tiled transverse Mercator zoom-levels scale sets

Longitude = Central Meridian + 4°

n

10°

15°

20°

25°

30°

35°

40°

0

155897

155900

155909

155923

155943

155966

155994

156024

156057

1

77948.7

77950.2

77954.6

77961.7

77971.3

77983.2

77996.9

78012.1

78028.3

2

38974.4

38975.1

38977.3

38980.8

38985.7

38991.6

38998.5

39006.1

39014.1

3

19487.2

19487.5

19488.6

19490.4

19492.8

19495.8

19499.2

19503.0

19507.1

4

9743.59

9743.77

9744.32

9745.21

9746.41

9747.90

9749.62

9751.51

9753.53

5

4871.80

4871.89

4872.16

4872.60

4873.21

4873.95

4874.81

4875.76

4876.77

6

2435.90

2435.94

2436.08

2436.30

2436.60

2436.97

2437.40

2437.88

2438.38

7

1217.95

1217.97

1218.04

1218.15

1218.30

1218.49

1218.70

1218.94

1219.19

8

608.974

608.986

609.020

609.075

609.151

609.244

609.351

609.470

609.596

9

304.487

304.493

304.510

304.538

304.575

304.622

304.675

304.735

304.798

10

152.244

152.246

152.255

152.269

152.288

152.311

152.338

152.367

152.399

11

76.1218

76.1232

76.1275

76.1344

76.1438

76.1554

76.1689

76.1837

76.1995

12

38.0609

38.0616

38.0637

38.0672

38.0719

38.0777

38.0844

38.0918

38.0997

13

19.0305

19.0308

19.0319

19.0336

19.0360

19.0389

19.0422

19.0459

19.0499

14

9.51523

9.51540

9.51594

9.51680

9.51798

9.51943

9.52111

9.52296

9.52494

15

4.75761

4.75770

4.75797

4.75840

4.75899

4.75972

4.76055

4.76148

4.76247

16

2.37881

2.37885

2.37898

2.37920

2.37950

2.37986

2.38028

2.38074

2.38123

17

1.18940

1.18943

1.18949

1.18960

1.18975

1.18993

1.19014

1.19037

1.19062

18

0.594702

0.594713

0.594746

0.594800

0.594874

0.594964

0.595069

0.595185

0.595308

19

0.297351

0.297356

0.297373

0.297400

0.297437

0.297482

0.297535

0.297593

0.297654

20

0.148675

0.148678

0.148687

0.148700

0.148718

0.148741

0.148767

0.148796

0.148827

21

0.0743377

0.0743391

0.0743433

0.0743500

0.0743592

0.0743706

0.0743837

0.0743981

0.0744136

22

0.0371688

0.0371695

0.0371716

0.0371750

0.0371796

0.0371853

0.0371918

0.0371991

0.0372068

23

0.0185844

0.0185848

0.0185858

0.0185875

0.0185898

0.0185926

0.0185959

0.0185995

0.0186034

24

0.00929221

0.00929239

0.00929291

0.00929375

0.00929490

0.00929632

0.00929796

0.00929977

0.00930170

Longitude = Central Meridian + 4°

n

45°

50°

55°

60°

65°

70°

75°

80°

85°

0

156090

156123

156155

156185

156213

156236

156255

156269

156278

1

78044.9

78061.5

78077.6

78092.7

78106.4

78118.1

78127.6

78134.6

78138.9

2

39022.5

39030.8

39038.8

39046.4

39053.2

39059.0

39063.8

39067.3

39069.5

3

19511.2

19515.4

19519.4

19523.2

19526.6

19529.5

19531.9

19533.7

19534.7

4

9755.62

9757.69

9759.71

9761.59

9763.29

9764.76

9765.95

9766.83

9767.36

5

4877.81

4878.85

4879.85

4880.80

4881.65

4882.38

4882.98

4883.41

4883.68

6

2438.90

2439.42

2439.93

2440.40

2440.82

2441.19

2441.49

2441.71

2441.84

7

1219.45

1219.71

1219.96

1220.20

1220.41

1220.60

1220.74

1220.85

1220.92

8

609.726

609.856

609.982

610.099

610.206

610.298

610.372

610.427

610.460

9

304.863

304.928

304.991

305.050

305.103

305.149

305.186

305.213

305.230

10

152.431

152.464

152.495

152.525

152.551

152.574

152.593

152.607

152.615

11

76.2157

76.2320

76.2477

76.2624

76.2757

76.2872

76.2965

76.3033

76.3075

12

38.1079

38.1160

38.1239

38.1312

38.1379

38.1436

38.1482

38.1517

38.1538

13

19.0539

19.0580

19.0619

19.0656

19.0689

19.0718

19.0741

19.0758

19.0769

14

9.52697

9.52900

9.53096

9.53280

9.53447

9.53590

9.53706

9.53792

9.53844

15

4.76348

4.76450

4.76548

4.76640

4.76723

4.76795

4.76853

4.76896

4.76922

16

2.38174

2.38225

2.38274

2.38320

2.38362

2.38398

2.38427

2.38448

2.38461

17

1.19087

1.19112

1.19137

1.19160

1.19181

1.19199

1.19213

1.19224

1.19231

18

0.595436

0.595562

0.595685

0.595800

0.595904

0.595994

0.596066

0.596120

0.596153

19

0.297718

0.297781

0.297843

0.297900

0.297952

0.297997

0.298033

0.298060

0.298076

20

0.148859

0.148891

0.148921

0.148950

0.148976

0.148998

0.149017

0.149030

0.149038

21

0.0744294

0.0744453

0.0744606

0.0744750

0.0744880

0.0744992

0.0745083

0.0745150

0.0745191

22

0.0372147

0.0372226

0.0372303

0.0372375

0.0372440

0.0372496

0.0372542

0.0372575

0.0372595

23

0.0186074

0.0186113

0.0186152

0.0186188

0.0186220

0.0186248

0.0186271

0.0186287

0.0186298

24

0.00930368

0.00930566

0.00930758

0.00930938

0.00931100

0.00931240

0.00931354

0.00931437

0.00931488

Table 3: Tiled transverse Mercator zoom-levels scale sets

Longitude = Central Meridian + 5°

n

10°

15°

20°

25°

30°

35°

40°

0

155682

155687

155700

155722

155753

155790

155833

155880

155931

1

77841.0

77843.3

77850.1

77861.2

77876.3

77894.9

77916.3

77940.1

77965.3

2

38920.5

38921.6

38925.1

38930.6

38938.1

38947.4

38958.2

38970.0

38982.7

3

19460.3

19460.8

19462.5

19465.3

19469.1

19473.7

19479.1

19485.0

19491.3

4

9730.13

9730.41

9731.26

9732.65

9734.54

9736.86

9739.54

9742.51

9745.66

5

4865.06

4865.21

4865.63

4866.33

4867.27

4868.43

4869.77

4871.25

4872.83

6

2432.53

2432.60

2432.82

2433.16

2433.63

2434.21

2434.89

2435.63

2436.42

7

1216.27

1216.30

1216.41

1216.58

1216.82

1217.11

1217.44

1217.81

1218.21

8

608.133

608.151

608.204

608.291

608.409

608.554

608.721

608.907

609.104

9

304.066

304.075

304.102

304.145

304.204

304.277

304.361

304.453

304.552

10

152.033

152.038

152.051

152.073

152.102

152.138

152.180

152.227

152.276

11

76.0166

76.0188

76.0255

76.0363

76.0511

76.0692

76.0902

76.1133

76.1380

12

38.0083

38.0094

38.0127

38.0182

38.0255

38.0346

38.0451

38.0567

38.0690

13

19.0042

19.0047

19.0064

19.0091

19.0128

19.0173

19.0225

19.0283

19.0345

14

9.50208

9.50236

9.50319

9.50454

9.50638

9.50865

9.51127

9.51417

9.51725

15

4.75104

4.75118

4.75159

4.75227

4.75319

4.75432

4.75564

4.75708

4.75863

16

2.37552

2.37559

2.37580

2.37614

2.37660

2.37716

2.37782

2.37854

2.37931

17

1.18776

1.18779

1.18790

1.18807

1.18830

1.18858

1.18891

1.18927

1.18966

18

0.593880

0.593897

0.593949

0.594034

0.594149

0.594291

0.594454

0.594635

0.594828

19

0.296940

0.296949

0.296975

0.297017

0.297074

0.297145

0.297227

0.297318

0.297414

20

0.148470

0.148474

0.148487

0.148508

0.148537

0.148573

0.148614

0.148659

0.148707

21

0.0742350

0.0742372

0.0742436

0.0742542

0.0742686

0.0742863

0.0743068

0.0743294

0.0743535

22

0.0371175

0.0371186

0.0371218

0.0371271

0.0371343

0.0371432

0.0371534

0.0371647

0.0371768

23

0.0185587

0.0185593

0.0185609

0.0185636

0.0185672

0.0185716

0.0185767

0.0185824

0.0185884

24

0.00927937

0.00927964

0.00928046

0.00928178

0.00928358

0.00928579

0.00928835

0.00929118

0.00929419

Longitude = Central Meridian + 5°

n

45°

50°

55°

60°

65°

70°

75°

80°

85°

0

155983

156035

156085

156132

156175

156211

156241

156263

156276

1

77991.3

78017.3

78042.4

78066.0

78087.3

78105.6

78120.5

78131.4

78138.1

2

38995.7

39008.6

39021.2

39033.0

39043.6

39052.8

39060.2

39065.7

39069.1

3

19497.8

19504.3

19510.6

19516.5

19521.8

19526.4

19530.1

19532.9

19534.5

4

9748.92

9752.16

9755.31

9758.25

9760.91

9763.20

9765.06

9766.43

9767.26

5

4874.46

4876.08

4877.65

4879.13

4880.45

4881.60

4882.53

4883.21

4883.63

6

2437.23

2438.04

2438.83

2439.56

2440.23

2440.80

2441.26

2441.61

2441.82

7

1218.61

1219.02

1219.41

1219.78

1220.11

1220.40

1220.63

1220.80

1220.91

8

609.307

609.510

609.707

609.891

610.057

610.200

610.316

610.402

610.454

9

304.654

304.755

304.853

304.945

305.028

305.100

305.158

305.201

305.227

10

152.327

152.378

152.427

152.473

152.514

152.550

152.579

152.600

152.613

11

76.1634

76.1888

76.2133

76.2363

76.2571

76.2750

76.2895

76.3002

76.3067

12

38.0817

38.0944

38.1067

38.1182

38.1285

38.1375

38.1448

38.1501

38.1534

13

19.0409

19.0472

19.0533

19.0591

19.0643

19.0688

19.0724

19.0751

19.0767

14

9.52043

9.52360

9.52667

9.52954

9.53214

9.53438

9.53619

9.53753

9.53834

15

4.76021

4.76180

4.76333

4.76477

4.76607

4.76719

4.76809

4.76876

4.76917

16

2.38011

2.38090

2.38167

2.38239

2.38303

2.38359

2.38405

2.38438

2.38459

17

1.19005

1.19045

1.19083

1.19119

1.19152

1.19180

1.19202

1.19219

1.19229

18

0.595027

0.595225

0.595417

0.595596

0.595759

0.595898

0.596012

0.596095

0.596146

19

0.297513

0.297612

0.297708

0.297798

0.297879

0.297949

0.298006

0.298048

0.298073

20

0.148757

0.148806

0.148854

0.148899

0.148940

0.148975

0.149003

0.149024

0.149037

21

0.0743783

0.0744031

0.0744271

0.0744495

0.0744698

0.0744873

0.0745015

0.0745119

0.0745183

22

0.0371892

0.0372015

0.0372135

0.0372248

0.0372349

0.0372437

0.0372507

0.0372560

0.0372592

23

0.0185946

0.0186008

0.0186068

0.0186124

0.0186175

0.0186218

0.0186254

0.0186280

0.0186296

24

0.00929729

0.00930039

0.00930338

0.00930619

0.00930873

0.00931091

0.00931269

0.00931399

0.00931479

Table 3: Tiled transverse Mercator zoom-levels scale sets

Longitude = Central Meridian + 6°

n

10°

15°

20°

25°

30°

35°

40°

0

155419

155425

155445

155477

155520

155574

155636

155704

155777

1

77709.4

77712.7

77722.5

77738.5

77760.2

77787.0

77817.9

77852.1

77888.5

2

38854.7

38856.4

38861.3

38869.3

38880.1

38893.5

38909.0

38926.0

38944.2

3

19427.4

19428.2

19430.6

19434.6

19440.1

19446.7

19454.5

19463.0

19472.1

4

9713.68

9714.09

9715.31

9717.32

9720.03

9723.37

9727.24

9731.51

9736.06

5

4856.84

4857.04

4857.66

4858.66

4860.02

4861.69

4863.62

4865.76

4868.03

6

2428.42

2428.52

2428.83

2429.33

2430.01

2430.84

2431.81

2432.88

2434.01

7

1214.21

1214.26

1214.41

1214.66

1215.00

1215.42

1215.90

1216.44

1217.01

8

607.105

607.131

607.207

607.332

607.502

607.711

607.952

608.219

608.504

9

303.552

303.565

303.604

303.666

303.751

303.855

303.976

304.110

304.252

10

151.776

151.783

151.802

151.833

151.875

151.928

151.988

152.055

152.126

11

75.8881

75.8913

75.9009

75.9165

75.9377

75.9638

75.9941

76.0274

76.0630

12

37.9440

37.9457

37.9504

37.9583

37.9689

37.9819

37.9970

38.0137

38.0315

13

18.9720

18.9728

18.9752

18.9791

18.9844

18.9910

18.9985

19.0069

19.0157

14

9.48601

9.48641

9.48761

9.48957

9.49222

9.49548

9.49926

9.50343

9.50787

15

4.74301

4.74321

4.74381

4.74478

4.74611

4.74774

4.74963

4.75171

4.75393

16

2.37150

2.37160

2.37190

2.37239

2.37305

2.37387

2.37481

2.37586

2.37697

17

1.18575

1.18580

1.18595

1.18620

1.18653

1.18694

1.18741

1.18793

1.18848

18

0.592876

0.592901

0.592976

0.593098

0.593264

0.593468

0.593704

0.593964

0.594242

19

0.296438

0.296450

0.296488

0.296549

0.296632

0.296734

0.296852

0.296982

0.297121

20

0.148219

0.148225

0.148244

0.148274

0.148316

0.148367

0.148426

0.148491

0.148560

21

0.0741095

0.0741126

0.0741220

0.0741372

0.0741579

0.0741834

0.0742129

0.0742455

0.0742802

22

0.0370547

0.0370563

0.0370610

0.0370686

0.0370790

0.0370917

0.0371065

0.0371228

0.0371401

23

0.0185274

0.0185282

0.0185305

0.0185343

0.0185395

0.0185459

0.0185532

0.0185614

0.0185701

24

0.00926368

0.00926408

0.00926525

0.00926716

0.00926974

0.00927293

0.00927662

0.00928069

0.00928503

Longitude = Central Meridian + 6°

n

45°

50°

55°

60°

65°

70°

75°

80°

85°

0

155852

155927

155999

156067

156128

156181

156223

156255

156274

1

77925.9

77963.3

77999.5

78033.4

78064.0

78090.4

78111.7

78127.5

78137.1

2

38963.0

38981.6

38999.7

39016.7

39032.0

39045.2

39055.9

39063.7

39068.6

3

19481.5

19490.8

19499.9

19508.3

19516.0

19522.6

19527.9

19531.9

19534.3

4

9740.74

9745.41

9749.94

9754.17

9758.00

9761.30

9763.97

9765.94

9767.14

5

4870.37

4872.71

4874.97

4877.09

4879.00

4880.65

4881.98

4882.97

4883.57

6

2435.18

2436.35

2437.48

2438.54

2439.50

2440.32

2440.99

2441.48

2441.78

7

1217.59

1218.18

1218.74

1219.27

1219.75

1220.16

1220.50

1220.74

1220.89

8

608.796

609.088

609.371

609.636

609.875

610.081

610.248

610.371

610.446

9

304.398

304.544

304.685

304.818

304.937

305.040

305.124

305.185

305.223

10

152.199

152.272

152.343

152.409

152.469

152.520

152.562

152.593

152.612

11

76.0995

76.1360

76.1714

76.2045

76.2344

76.2601

76.2810

76.2964

76.3058

12

38.0498

38.0680

38.0857

38.1022

38.1172

38.1301

38.1405

38.1482

38.1529

13

19.0249

19.0340

19.0428

19.0511

19.0586

19.0650

19.0702

19.0741

19.0764

14

9.51244

9.51700

9.52142

9.52556

9.52930

9.53252

9.53512

9.53705

9.53822

15

4.75622

4.75850

4.76071

4.76278

4.76465

4.76626

4.76756

4.76852

4.76911

16

2.37811

2.37925

2.38036

2.38139

2.38232

2.38313

2.38378

2.38426

2.38456

17

1.18905

1.18963

1.19018

1.19069

1.19116

1.19156

1.19189

1.19213

1.19228

18

0.594527

0.594813

0.595089

0.595347

0.595581

0.595782

0.595945

0.596065

0.596139

19

0.297264

0.297406

0.297544

0.297674

0.297790

0.297891

0.297973

0.298033

0.298069

20

0.148632

0.148703

0.148772

0.148837

0.148895

0.148946

0.148986

0.149016

0.149035

21

0.0743159

0.0743516

0.0743861

0.0744184

0.0744476

0.0744728

0.0744932

0.0745082

0.0745174

22

0.0371580

0.0371758

0.0371931

0.0372092

0.0372238

0.0372364

0.0372466

0.0372541

0.0372587

23

0.0185790

0.0185879

0.0185965

0.0186046

0.0186119

0.0186182

0.0186233

0.0186270

0.0186293

24

0.00928949

0.00929395

0.00929826

0.00930230

0.00930595

0.00930910

0.00931165

0.00931352

0.00931467

Table 3: Tiled transverse Mercator zoom-levels scale sets

Longitude = Central Meridian + 7°

n

10°

15°

20°

25°

30°

35°

40°

0

155108

155117

155144

155187

155246

155319

155403

155497

155596

1

77554.0

77558.5

77571.8

77593.6

77623.2

77659.6

77701.7

77748.3

77797.8

2

38777.0

38779.2

38785.9

38796.8

38811.6

38829.8

38850.9

38874.1

38898.9

3

19388.5

19389.6

19393.0

19398.4

19405.8

19414.9

19425.4

19437.1

19449.4

4

9694.25

9694.81

9696.48

9699.21

9702.90

9707.45

9712.72

9718.53

9724.72

5

4847.12

4847.40

4848.24

4849.60

4851.45

4853.73

4856.36

4859.27

4862.36

6

2423.56

2423.70

2424.12

2424.80

2425.73

2426.86

2428.18

2429.63

2431.18

7

1211.78

1211.85

1212.06

1212.40

1212.86

1213.43

1214.09

1214.82

1215.59

8

605.890

605.926

606.030

606.200

606.431

606.716

607.045

607.408

607.795

9

302.945

302.963

303.015

303.100

303.216

303.358

303.522

303.704

303.897

10

151.473

151.481

151.507

151.550

151.608

151.679

151.761

151.852

151.949

11

75.7363

75.7407

75.7537

75.7750

75.8039

75.8395

75.8806

75.9260

75.9744

12

37.8681

37.8703

37.8769

37.8875

37.9020

37.9197

37.9403

37.9630

37.9872

13

18.9341

18.9352

18.9384

18.9438

18.9510

18.9599

18.9702

18.9815

18.9936

14

9.46704

9.46759

9.46922

9.47188

9.47549

9.47993

9.48508

9.49075

9.49680

15

4.73352

4.73379

4.73461

4.73594

4.73774

4.73997

4.74254

4.74538

4.74840

16

2.36676

2.36690

2.36730

2.36797

2.36887

2.36998

2.37127

2.37269

2.37420

17

1.18338

1.18345

1.18365

1.18399

1.18444

1.18499

1.18563

1.18634

1.18710

18

0.591690

0.591724

0.591826

0.591993

0.592218

0.592496

0.592817

0.593172

0.593550

19

0.295845

0.295862

0.295913

0.295996

0.296109

0.296248

0.296409

0.296586

0.296775

20

0.147922

0.147931

0.147957

0.147998

0.148055

0.148124

0.148204

0.148293

0.148387

21

0.0739612

0.0739655

0.0739783

0.0739991

0.0740273

0.0740620

0.0741022

0.0741465

0.0741937

22

0.0369806

0.0369828

0.0369891

0.0369995

0.0370136

0.0370310

0.0370511

0.0370733

0.0370969

23

0.0184903

0.0184914

0.0184946

0.0184998

0.0185068

0.0185155

0.0185255

0.0185366

0.0185484

24

0.00924515

0.00924569

0.00924728

0.00924988

0.00925341

0.00925775

0.00926277

0.00926831

0.00927422

Longitude = Central Meridian + 7°

n

45°

50°

55°

60°

65°

70°

75°

80°

85°

0

155697

155799

155898

155990

156073

156145

156203

156246

156272

1

77848.7

77899.6

77948.8

77994.9

78036.5

78072.4

78101.5

78122.9

78135.9

2

38924.4

38949.8

38974.4

38997.5

39018.3

39036.2

39050.7

39061.4

39068.0

3

19462.2

19474.9

19487.2

19498.7

19509.1

19518.1

19525.4

19530.7

19534.0

4

9731.09

9737.45

9743.60

9749.36

9754.57

9759.05

9762.68

9765.36

9766.99

5

4865.54

4868.72

4871.80

4874.68

4877.28

4879.52

4881.34

4882.68

4883.50

6

2432.77

2434.36

2435.90

2437.34

2438.64

2439.76

2440.67

2441.34

2441.75

7

1216.39

1217.18

1217.95

1218.67

1219.32

1219.88

1220.34

1220.67

1220.87

8

608.193

608.590

608.975

609.335

609.660

609.941

610.168

610.335

610.437

9

304.097

304.295

304.488

304.668

304.830

304.970

305.084

305.167

305.219

10

152.048

152.148

152.244

152.334

152.415

152.485

152.542

152.584

152.609

11

76.0241

76.0738

76.1219

76.1669

76.2075

76.2426

76.2710

76.2918

76.3046

12

38.0121

38.0369

38.0609

38.0835

38.1038

38.1213

38.1355

38.1459

38.1523

13

19.0060

19.0185

19.0305

19.0417

19.0519

19.0606

19.0677

19.0730

19.0762

14

9.50302

9.50923

9.51523

9.52086

9.52594

9.53032

9.53387

9.53648

9.53808

15

4.75151

4.75461

4.75762

4.76043

4.76297

4.76516

4.76693

4.76824

4.76904

16

2.37575

2.37731

2.37881

2.38022

2.38149

2.38258

2.38347

2.38412

2.38452

17

1.18788

1.18865

1.18940

1.19011

1.19074

1.19129

1.19173

1.19206

1.19226

18

0.593939

0.594327

0.594702

0.595054

0.595371

0.595645

0.595867

0.596030

0.596130

19

0.296969

0.297163

0.297351

0.297527

0.297686

0.297823

0.297933

0.298015

0.298065

20

0.148485

0.148582

0.148676

0.148763

0.148843

0.148911

0.148967

0.149008

0.149032

21

0.0742423

0.0742908

0.0743378

0.0743817

0.0744214

0.0744556

0.0744834

0.0745038

0.0745162

22

0.0371212

0.0371454

0.0371689

0.0371909

0.0372107

0.0372278

0.0372417

0.0372519

0.0372581

23

0.0185606

0.0185727

0.0185844

0.0185954

0.0186054

0.0186139

0.0186208

0.0186259

0.0186291

24

0.00928029

0.00928635

0.00929222

0.00929772

0.00930268

0.00930695

0.00931042

0.00931297

0.00931453

Table 3: Tiled transverse Mercator zoom-levels scale sets

Longitude = Central Meridian + 8°

n

10°

15°

20°

25°

30°

35°

40°

0

154749

154761

154796

154853

154931

155026

155136

155257

155387

1

77374.7

77380.6

77398.1

77426.6

77465.3

77512.8

77567.9

77628.6

77693.3

2

38687.4

38690.3

38699.1

38713.3

38732.6

38756.4

38783.9

38814.3

38846.6

3

19343.7

19345.2

19349.5

19356.7

19366.3

19378.2

19392.0

19407.2

19423.3

4

9671.84

9672.58

9674.76

9678.33

9683.16

9689.10

9695.98

9703.58

9711.66

5

4835.92

4836.29

4837.38

4839.16

4841.58

4844.55

4847.99

4851.79

4855.83

6

2417.96

2418.14

2418.69

2419.58

2420.79

2422.28

2424.00

2425.89

2427.91

7

1208.98

1209.07

1209.35

1209.79

1210.39

1211.14

1212.00

1212.95

1213.96

8

604.490

604.536

604.673

604.895

605.197

605.569

605.999

606.474

606.979

9

302.245

302.268

302.336

302.448

302.599

302.784

302.999

303.237

303.489

10

151.123

151.134

151.168

151.224

151.299

151.392

151.500

151.618

151.745

11

75.5613

75.5670

75.5841

75.6119

75.6497

75.6961

75.7499

75.8092

75.8723

12

37.7806

37.7835

37.7920

37.8060

37.8248

37.8481

37.8749

37.9046

37.9362

13

18.8903

18.8918

18.8960

18.9030

18.9124

18.9240

18.9375

18.9523

18.9681

14

9.44516

9.44588

9.44801

9.45149

9.45621

9.46201

9.46873

9.47615

9.48404

15

4.72258

4.72294

4.72401

4.72575

4.72810

4.73101

4.73437

4.73808

4.74202

16

2.36129

2.36147

2.36200

2.36287

2.36405

2.36550

2.36718

2.36904

2.37101

17

1.18064

1.18073

1.18100

1.18144

1.18203

1.18275

1.18359

1.18452

1.18551

18

0.590322

0.590367

0.590501

0.590718

0.591013

0.591376

0.591796

0.592259

0.592753

19

0.295161

0.295184

0.295250

0.295359

0.295506

0.295688

0.295898

0.296130

0.296376

20

0.147581

0.147592

0.147625

0.147680

0.147753

0.147844

0.147949

0.148065

0.148188

21

0.0737903

0.0737959

0.0738126

0.0738398

0.0738766

0.0739220

0.0739745

0.0740324

0.0740941

22

0.0368952

0.0368980

0.0369063

0.0369199

0.0369383

0.0369610

0.0369872

0.0370162

0.0370470

23

0.0184476

0.0184490

0.0184531

0.0184599

0.0184692

0.0184805

0.0184936

0.0185081

0.0185235

24

0.00922379

0.00922449

0.00922657

0.00922997

0.00923458

0.00924025

0.00924681

0.00925405

0.00926176

Longitude = Central Meridian + 8°

n

45°

50°

55°

60°

65°

70°

75°

80°

85°

0

155520

155652

155781

155901

156010

156103

156179

156235

156269

1

77759.8

77826.2

77890.5

77950.6

78004.9

78051.7

78089.6

78117.5

78134.6

2

38879.9

38913.1

38945.2

38975.3

39002.5

39025.9

39044.8

39058.8

39067.3

3

19440.0

19456.6

19472.6

19487.7

19501.2

19512.9

19522.4

19529.4

19533.7

4

9719.98

9728.28

9736.31

9743.83

9750.62

9756.46

9761.20

9764.69

9766.83

5

4859.99

4864.14

4868.15

4871.91

4875.31

4878.23

4880.60

4882.35

4883.41

6

2429.99

2432.07

2434.08

2435.96

2437.65

2439.12

2440.30

2441.17

2441.71

7

1215.00

1216.03

1217.04

1217.98

1218.83

1219.56

1220.15

1220.59

1220.85

8

607.498

608.017

608.519

608.989

609.413

609.779

610.075

610.293

610.427

9

303.749

304.009

304.260

304.495

304.707

304.890

305.038

305.147

305.213

10

151.875

152.004

152.130

152.247

152.353

152.445

152.519

152.573

152.607

11

75.9373

76.0022

76.0649

76.1237

76.1767

76.2224

76.2594

76.2867

76.3033

12

37.9687

38.0011

38.0324

38.0618

38.0883

38.1112

38.1297

38.1433

38.1517

13

18.9843

19.0005

19.0162

19.0309

19.0442

19.0556

19.0649

19.0717

19.0758

14

9.49216

9.50027

9.50811

9.51546

9.52209

9.52780

9.53243

9.53583

9.53792

15

4.74608

4.75013

4.75406

4.75773

4.76104

4.76390

4.76621

4.76792

4.76896

16

2.37304

2.37507

2.37703

2.37886

2.38052

2.38195

2.38311

2.38396

2.38448

17

1.18652

1.18753

1.18851

1.18943

1.19026

1.19097

1.19155

1.19198

1.19224

18

0.593260

0.593767

0.594257

0.594716

0.595130

0.595487

0.595777

0.595989

0.596120

19

0.296630

0.296883

0.297129

0.297358

0.297565

0.297744

0.297888

0.297995

0.298060

20

0.148315

0.148442

0.148564

0.148679

0.148783

0.148872

0.148944

0.148997

0.149030

21

0.0741575

0.0742208

0.0742821

0.0743395

0.0743913

0.0744359

0.0744721

0.0744987

0.0745150

22

0.0370788

0.0371104

0.0371411

0.0371698

0.0371956

0.0372180

0.0372360

0.0372493

0.0372575

23

0.0185394

0.0185552

0.0185705

0.0185849

0.0185978

0.0186090

0.0186180

0.0186247

0.0186287

24

0.00926969

0.00927761

0.00928527

0.00929244

0.00929891

0.00930449

0.00930901

0.00931234

0.00931437

Table 3: Tiled transverse Mercator zoom-levels scale sets

Longitude = Central Meridian + 9°

N

10°

15°

20°

25°

30°

35°

40°

0

154344

154358

154403

154475

154573

154693

154833

154987

155150

1

77171.8

77179.2

77201.4

77237.5

77286.4

77346.7

77416.3

77493.3

77575.1

2

38585.9

38589.6

38600.7

38618.7

38643.2

38673.3

38708.2

38746.6

38787.5

3

19292.9

19294.8

19300.3

19309.4

19321.6

19336.7

19354.1

19373.3

19393.8

4

9646.47

9647.41

9650.17

9654.69

9660.80

9668.33

9677.04

9686.66

9696.88

5

4823.24

4823.70

4825.09

4827.34

4830.40

4834.17

4838.52

4843.33

4848.44

6

2411.62

2411.85

2412.54

2413.67

2415.20

2417.08

2419.26

2421.66

2424.22

7

1205.81

1205.93

1206.27

1206.84

1207.60

1208.54

1209.63

1210.83

1212.11

8

602.905

602.963

603.136

603.418

603.800

604.271

604.815

605.416

606.055

9

301.452

301.481

301.568

301.709

301.900

302.135

302.408

302.708

303.028

10

150.726

150.741

150.784

150.854

150.950

151.068

151.204

151.354

151.514

11

75.3631

75.3704

75.3920

75.4272

75.4750

75.5339

75.6019

75.6770

75.7569

12

37.6815

37.6852

37.6960

37.7136

37.7375

37.7669

37.8009

37.8385

37.8785

13

18.8408

18.8426

18.8480

18.8568

18.8688

18.8835

18.9005

18.9193

18.9392

14

9.42039

9.42130

9.42400

9.42840

9.43438

9.44173

9.45024

9.45963

9.46961

15

4.71019

4.71065

4.71200

4.71420

4.71719

4.72087

4.72512

4.72981

4.73481

16

2.35510

2.35532

2.35600

2.35710

2.35859

2.36043

2.36256

2.36491

2.36740

17

1.17755

1.17766

1.17800

1.17855

1.17930

1.18022

1.18128

1.18245

1.18370

18

0.588774

0.588831

0.589000

0.589275

0.589649

0.590108

0.590640

0.591227

0.591851

19

0.294387

0.294415

0.294500

0.294638

0.294824

0.295054

0.295320

0.295613

0.295925

20

0.147194

0.147208

0.147250

0.147319

0.147412

0.147527

0.147660

0.147807

0.147963

21

0.0735968

0.0736039

0.0736250

0.0736594

0.0737061

0.0737635

0.0738300

0.0739033

0.0739813

22

0.0367984

0.0368019

0.0368125

0.0368297

0.0368530

0.0368818

0.0369150

0.0369517

0.0369907

23

0.0183992

0.0184010

0.0184062

0.0184149

0.0184265

0.0184409

0.0184575

0.0184758

0.0184953

24

0.00919959

0.00920048

0.00920312

0.00920743

0.00921326

0.00922044

0.00922875

0.00923792

0.00924767

Longitude = Central Meridian + 9°

n

45°

50°

55°

60°

65°

70°

75°

80°

85°

0

155318

155486

155649

155801

155938

156057

156153

156223

156266

1

77659.2

77743.2

77824.5

77900.6

77969.2

78028.3

78076.3

78111.5

78133.1

2

38829.6

38871.6

38912.2

38950.3

38984.6

39014.2

39038.1

39055.8

39066.5

3

19414.8

19435.8

19456.1

19475.1

19492.3

19507.1

19519.1

19527.9

19533.3

4

9707.41

9717.90

9728.06

9737.57

9746.15

9753.54

9759.53

9763.94

9766.64

5

4853.70

4858.95

4864.03

4868.79

4873.08

4876.77

4879.77

4881.97

4883.32

6

2426.85

2429.48

2432.02

2434.39

2436.54

2438.39

2439.88

2440.98

2441.66

7

1213.43

1214.74

1216.01

1217.20

1218.27

1219.19

1219.94

1220.49

1220.83

8

606.713

607.369

608.004

608.598

609.134

609.596

609.971

610.246

610.415

9

303.356

303.685

304.002

304.299

304.567

304.798

304.985

305.123

305.207

10

151.678

151.842

152.001

152.150

152.284

152.399

152.493

152.562

152.604

11

75.8391

75.9211

76.0005

76.0748

76.1418

76.1996

76.2463

76.2808

76.3018

12

37.9196

37.9606

38.0002

38.0374

38.0709

38.0998

38.1232

38.1404

38.1509

13

18.9598

18.9803

19.0001

19.0187

19.0355

19.0499

19.0616

19.0702

19.0755

14

9.47989

9.49014

9.50006

9.50935

9.51773

9.52494

9.53079

9.53510

9.53773

15

4.73994

4.74507

4.75003

4.75467

4.75886

4.76247

4.76540

4.76755

4.76887

16

2.36997

2.37254

2.37502

2.37734

2.37943

2.38124

2.38270

2.38377

2.38443

17

1.18499

1.18627

1.18751

1.18867

1.18972

1.19062

1.19135

1.19189

1.19222

18

0.592493

0.593134

0.593754

0.594334

0.594858

0.595309

0.595675

0.595944

0.596108

19

0.296247

0.296567

0.296877

0.297167

0.297429

0.297655

0.297837

0.297972

0.298054

20

0.148123

0.148283

0.148438

0.148584

0.148714

0.148827

0.148919

0.148986

0.149027

21

0.0740616

0.0741417

0.0742192

0.0742918

0.0743572

0.0744136

0.0744593

0.0744929

0.0745135

22

0.0370308

0.0370709

0.0371096

0.0371459

0.0371786

0.0372068

0.0372297

0.0372465

0.0372568

23

0.0185154

0.0185354

0.0185548

0.0185729

0.0185893

0.0186034

0.0186148

0.0186232

0.0186284

24

0.00925770

0.00926772

0.00927740

0.00928647

0.00929465

0.00930170

0.00930741

0.00931162

0.00931419

Table 3: Tiled transverse Mercator zoom-levels scale sets

Longitude = Central Meridian + 10°

n

10°

15°

20°

25°

30°

35°

40°

0

153890

153909

153963

154053

154174

154322

154495

154685

154886

1

76945.2

76954.4

76981.7

77026.3

77086.8

77161.2

77247.3

77342.3

77443.2

2

38472.6

38477.2

38490.9

38513.2

38543.4

38580.6

38623.6

38671.1

38721.6

3

19236.3

19238.6

19245.4

19256.6

19271.7

19290.3

19311.8

19335.6

19360.8

4

9618.15

9619.30

9622.72

9628.29

9635.85

9645.15

9655.91

9667.78

9680.40

5

4809.07

4809.65

4811.36

4814.15

4817.93

4822.58

4827.95

4833.89

4840.20

6

2404.54

2404.82

2405.68

2407.07

2408.96

2411.29

2413.98

2416.95

2420.10

7

1202.27

1202.41

1202.84

1203.54

1204.48

1205.64

1206.99

1208.47

1210.05

8

601.134

601.206

601.420

601.768

602.241

602.822

603.494

604.236

605.025

9

300.567

300.603

300.710

300.884

301.120

301.411

301.747

302.118

302.513

10

150.284

150.302

150.355

150.442

150.560

150.706

150.874

151.059

151.256

11

75.1418

75.1508

75.1775

75.2210

75.2801

75.3528

75.4368

75.5295

75.6282

12

37.5709

37.5754

37.5887

37.6105

37.6400

37.6764

37.7184

37.7648

37.8141

13

18.7854

18.7877

18.7944

18.8053

18.8200

18.8382

18.8592

18.8824

18.9070

14

9.39272

9.39385

9.39718

9.40263

9.41001

9.41910

9.42960

9.44119

9.45352

15

4.69636

4.69692

4.69859

4.70131

4.70501

4.70955

4.71480

4.72060

4.72676

16

2.34818

2.34846

2.34930

2.35066

2.35250

2.35477

2.35740

2.36030

2.36338

17

1.17409

1.17423

1.17465

1.17533

1.17625

1.17739

1.17870

1.18015

1.18169

18

0.587045

0.587115

0.587324

0.587664

0.588126

0.588693

0.589350

0.590075

0.590845

19

0.293523

0.293558

0.293662

0.293832

0.294063

0.294347

0.294675

0.295037

0.295423

20

0.146761

0.146779

0.146831

0.146916

0.147031

0.147173

0.147337

0.147519

0.147711

21

0.0733806

0.0733894

0.0734155

0.0734580

0.0735157

0.0735867

0.0736687

0.0737593

0.0738556

22

0.0366903

0.0366947

0.0367077

0.0367290

0.0367579

0.0367933

0.0368344

0.0368797

0.0369278

23

0.0183452

0.0183474

0.0183539

0.0183645

0.0183789

0.0183967

0.0184172

0.0184398

0.0184639

24

0.00917258

0.00917368

0.00917694

0.00918226

0.00918946

0.00919834

0.00920859

0.00921992

0.00923195

Longitude = Central Meridian + 10°

n

45°

50°

55°

60°

65°

70°

75°

80°

85°

0

155094

155302

155502

155690

155859

156005

156123

156210

156263

1

77547.1

77650.8

77751.0

77844.8

77929.4

78002.3

78061.4

78104.8

78131.4

2

38773.6

38825.4

38875.5

38922.4

38964.7

39001.2

39030.7

39052.4

39065.7

3

19386.8

19412.7

19437.7

19461.2

19482.4

19500.6

19515.3

19526.2

19532.9

4

9693.39

9706.34

9718.87

9730.60

9741.18

9750.29

9757.67

9763.10

9766.43

5

4846.70

4853.17

4859.44

4865.30

4870.59

4875.14

4878.84

4881.55

4883.21

6

2423.35

2426.59

2429.72

2432.65

2435.29

2437.57

2439.42

2440.78

2441.61

7

1211.67

1213.29

1214.86

1216.32

1217.65

1218.79

1219.71

1220.39

1220.80

8

605.837

606.646

607.430

608.162

608.824

609.393

609.854

610.194

610.402

9

302.918

303.323

303.715

304.081

304.412

304.697

304.927

305.097

305.201

10

151.459

151.662

151.857

152.041

152.206

152.348

152.464

152.548

152.600

11

75.7296

75.8308

75.9287

76.0203

76.1029

76.1741

76.2318

76.2742

76.3002

12

37.8648

37.9154

37.9643

38.0102

38.0515

38.0871

38.1159

38.1371

38.1501

13

18.9324

18.9577

18.9822

19.0051

19.0257

19.0435

19.0580

19.0686

19.0751

14

9.46620

9.47885

9.49109

9.50254

9.51287

9.52177

9.52898

9.53428

9.53753

15

4.73310

4.73943

4.74554

4.75127

4.75643

4.76088

4.76449

4.76714

4.76876

16

2.36655

2.36971

2.37277

2.37563

2.37822

2.38044

2.38224

2.38357

2.38438

17

1.18328

1.18486

1.18639

1.18782

1.18911

1.19022

1.19112

1.19178

1.19219

18

0.591638

0.592428

0.593193

0.593909

0.594554

0.595110

0.595561

0.595892

0.596095

19

0.295819

0.296214

0.296596

0.296954

0.297277

0.297555

0.297780

0.297946

0.298048

20

0.147909

0.148107

0.148298

0.148477

0.148639

0.148778

0.148890

0.148973

0.149024

21

0.0739547

0.0740535

0.0741491

0.0742386

0.0743193

0.0743888

0.0744451

0.0744866

0.0745119

22

0.0369774

0.0370268

0.0370746

0.0371193

0.0371596

0.0371944

0.0372226

0.0372433

0.0372560

23

0.0184887

0.0185134

0.0185373

0.0185596

0.0185798

0.0185972

0.0186113

0.0186216

0.0186280

24

0.00924434

0.00925669

0.00926864

0.00927982

0.00928991

0.00929860

0.00930564

0.00931082

0.00931399

Table 4: Tiled polar stereographic zoom-levels scale sets

 

n

0

72507.7

73764.6

75021.0

76276.5

77530.7

78783.2

80033.8

81281.9

82527.3

83769.5

1

36253.9

36882.3

37510.5

38138.2

38765.3

39391.6

40016.9

40641.0

41263.6

41884.8

2

18126.9

18441.2

18755.2

19069.1

19382.7

19695.8

20008.4

20320.5

20631.8

20942.4

3

9063.47

9220.58

9377.62

9534.56

9691.33

9847.90

10004.2

10160.2

10315.9

10471.2

4

4531.73

4610.29

4688.81

4767.28

4845.67

4923.95

5002.11

5080.12

5157.96

5235.60

5

2265.87

2305.14

2344.41

2383.64

2422.83

2461.98

2501.05

2540.06

2578.98

2617.80

6

1132.93

1152.57

1172.20

1191.82

1211.42

1230.99

1250.53

1270.03

1289.49

1308.90

7

566.467

576.286

586.102

595.910

605.708

615.494

625.264

635.015

644.744

654.449

8

283.233

288.143

293.051

297.955

302.854

307.747

312.632

317.507

322.372

327.225

9

141.617

144.072

146.525

148.977

151.427

153.873

156.316

158.754

161.186

163.612

10

70.8083

72.0358

73.2627

74.4887

75.7135

76.9367

78.1580

79.3769

80.5931

81.8062

11

35.4042

36.0179

36.6313

37.2444

37.8568

38.4684

39.0790

39.6884

40.2965

40.9031

12

17.7021

18.0089

18.3157

18.6222

18.9284

19.2342

19.5395

19.8442

20.1483

20.4515

13

8.85104

9.00447

9.15784

9.31109

9.46419

9.61709

9.76975

9.92211

10.0741

10.2258

14

4.42552

4.50224

4.57892

4.65555

4.73210

4.80855

4.88487

4.96105

5.03707

5.11289

15

2.21276

2.25112

2.28946

2.32777

2.36605

2.40427

2.44244

2.48053

2.51853

2.55644

16

1.10638

1.12556

1.14473

1.16389

1.18302

1.20214

1.22122

1.24026

1.25927

1.27822

17

0.553190

0.562779

0.572365

0.581943

0.591512

0.601068

0.610609

0.620132

0.629633

0.639111

18

0.276595

0.281390

0.286182

0.290972

0.295756

0.300534

0.305305

0.310066

0.314817

0.319555

19

0.138298

0.140695

0.143091

0.145486

0.147878

0.150267

0.152652

0.155033

0.157408

0.159778

20

0.0691488

0.0703474

0.0715456

0.0727429

0.0739390

0.0751335

0.0763261

0.0775165

0.0787042

0.0798889

21

0.0345744

0.0351737

0.0357728

0.0363715

0.0369695

0.0375668

0.0381631

0.0387582

0.0393521

0.0399444

22

0.0172872

0.0175869

0.0178864

0.0181857

0.0184848

0.0187834

0.0190815

0.0193791

0.0196760

0.0199722

23

0.00864360

0.00879343

0.00894320

0.00909286

0.00924238

0.00939169

0.00954077

0.00968956

0.00983802

0.00998611

24

0.00432180

0.00439671

0.00447160

0.00454643

0.00462119

0.00469585

0.00477038

0.00484478

0.00491901

0.00499305

n

10°

11°

12°

13°

14°

15°

16°

17°

18°

19°

0

85008.3

86243.1

87473.8

88699.8

89920.8

91136.5

92346.5

93550.4

94748.0

95938.7

1

42504.1

43121.6

43736.9

44349.9

44960.4

45568.3

46173.3

46775.2

47374.0

47969.3

2

21252.1

21560.8

21868.4

22174.9

22480.2

22784.1

23086.6

23387.6

23687.0

23984.7

3

10626.0

10780.4

10934.2

11087.5

11240.1

11392.1

11543.3

11693.8

11843.5

11992.3

4

5313.02

5390.20

5467.11

5543.74

5620.05

5696.03

5771.66

5846.90

5921.75

5996.17

5

2656.51

2695.10

2733.56

2771.87

2810.03

2848.02

2885.83

2923.45

2960.87

2998.08

6

1328.25

1347.55

1366.78

1385.93

1405.01

1424.01

1442.91

1461.73

1480.44

1499.04

7

664.127

673.775

683.389

692.967

702.506

712.004

721.457

730.863

740.218

749.521

8

332.064

336.887

341.694

346.484

351.253

356.002

360.729

365.431

370.109

374.760

9

166.032

168.444

170.847

173.242

175.627

178.001

180.364

182.716

185.055

187.380

10

83.0159

84.2218

85.4236

86.6209

87.8133

89.0005

90.1821

91.3579

92.5273

93.6901

11

41.5079

42.1109

42.7118

43.3104

43.9067

44.5003

45.0911

45.6789

46.2637

46.8451

12

20.7540

21.0555

21.3559

21.6552

21.9533

22.2501

22.5455

22.8395

23.1318

23.4225

13

10.3770

10.5277

10.6780

10.8276

10.9767

11.1251

11.2728

11.4197

11.5659

11.7113

14

5.18849

5.26386

5.33898

5.41381

5.48833

5.56253

5.63638

5.70987

5.78296

5.85563

15

2.59425

2.63193

2.66949

2.70690

2.74417

2.78127

2.81819

2.85493

2.89148

2.92782

16

1.29712

1.31597

1.33474

1.35345

1.37208

1.39063

1.40910

1.42747

1.44574

1.46391

17

0.648562

0.657983

0.667372

0.676726

0.686041

0.695316

0.704548

0.713733

0.722870

0.731954

18

0.324281

0.328991

0.333686

0.338363

0.343021

0.347658

0.352274

0.356867

0.361435

0.365977

19

0.162140

0.164496

0.166843

0.169181

0.171510

0.173829

0.176137

0.178433

0.180717

0.182989

20

0.0810702

0.0822479

0.0834215

0.0845907

0.0857552

0.0869146

0.0880685

0.0892167

0.0903587

0.0914943

21

0.0405351

0.0411239

0.0417107

0.0422954

0.0428776

0.0434573

0.0440343

0.0446083

0.0451793

0.0457471

22

0.0202676

0.0205620

0.0208554

0.0211477

0.0214388

0.0217286

0.0220171

0.0223042

0.0225897

0.0228736

23

0.0101338

0.0102810

0.0104277

0.0105738

0.0107194

0.0108643

0.0110086

0.0111521

0.0112948

0.0114368

24

0.00506689

0.00514049

0.00521384

0.00528692

0.00535970

0.00543216

0.00550428

0.00557604

0.00564742

0.00571839

Table 4: Tiled polar stereographic zoom-levels scale sets

 

n

20°

21°

22°

23°

24°

25°

26°

27°

28°

29°

0

97122.3

98298.4

99466.6

100627

101778

102921

104054

105178

106292

107396

1

48561.1

49149.2

49733.3

50313.3

50889.1

51460.4

52027.1

52589.0

53146.0

53697.8

2

24280.6

24574.6

24866.7

25156.7

25444.6

25730.2

26013.6

26294.5

26573.0

26848.9

3

12140.3

12287.3

12433.3

12578.3

12722.3

12865.1

13006.8

13147.3

13286.5

13424.5

4

6070.14

6143.65

6216.66

6289.17

6361.14

6432.55

6503.39

6573.63

6643.25

6712.23

5

3035.07

3071.82

3108.33

3144.58

3180.57

3216.28

3251.70

3286.81

3321.62

3356.11

6

1517.54

1535.91

1554.17

1572.29

1590.28

1608.14

1625.85

1643.41

1660.81

1678.06

7

758.768

767.956

777.083

786.146

795.142

804.069

812.924

821.704

830.406

839.029

8

379.384

383.978

388.542

393.073

397.571

402.035

406.462

410.852

415.203

419.514

9

189.692

191.989

194.271

196.536

198.786

201.017

203.231

205.426

207.602

209.757

10

94.8460

95.9945

97.1354

98.2682

99.3928

100.509

101.615

102.713

103.801

104.879

11

47.4230

47.9973

48.5677

49.1341

49.6964

50.2543

50.8077

51.3565

51.9004

52.4393

12

23.7115

23.9986

24.2838

24.5671

24.8482

25.1272

25.4039

25.6782

25.9502

26.2196

13

11.8557

11.9993

12.1419

12.2835

12.4241

12.5636

12.7019

12.8391

12.9751

13.1098

14

5.92787

5.99966

6.07096

6.14177

6.21205

6.28179

6.35097

6.41956

6.48755

6.55491

15

2.96394

2.99983

3.03548

3.07088

3.10602

3.14089

3.17548

3.20978

3.24377

3.27746

16

1.48197

1.49991

1.51774

1.53544

1.55301

1.57045

1.58774

1.60489

1.62189

1.63873

17

0.740984

0.749957

0.758870

0.767721

0.776506

0.785224

0.793871

0.802445

0.810944

0.819364

18

0.370492

0.374979

0.379435

0.383860

0.388253

0.392612

0.396935

0.401223

0.405472

0.409682

19

0.185246

0.187489

0.189718

0.191930

0.194127

0.196306

0.198468

0.200611

0.202736

0.204841

20

0.0926230

0.0937446

0.0948588

0.0959651

0.0970633

0.0981530

0.0992339

0.100306

0.101368

0.102420

21

0.0463115

0.0468723

0.0474294

0.0479825

0.0485316

0.0490765

0.0496169

0.0501528

0.0506840

0.0512102

22

0.0231558

0.0234362

0.0237147

0.0239913

0.0242658

0.0245382

0.0248085

0.0250764

0.0253420

0.0256051

23

0.0115779

0.0117181

0.0118573

0.0119956

0.0121329

0.0122691

0.0124042

0.0125382

0.0126710

0.0128026

24

0.00578894

0.00585904

0.00592867

0.00599782

0.00606645

0.00613456

0.00620212

0.00626910

0.00633550

0.00640128

n

30°

31°

32°

33°

34°

35°

36°

37°

38°

39°

0

108489

109571

110642

111701

112749

113784

114807

115817

116814

117797

1

54244.4

54785.5

55321.0

55850.7

56374.5

56892.1

57403.5

57908.6

58407.0

58898.7

2

27122.2

27392.7

27660.5

27925.3

28187.2

28446.1

28701.8

28954.3

29203.5

29449.4

3

13561.1

13696.4

13830.2

13962.7

14093.6

14223.0

14350.9

14477.1

14601.8

14724.7

4

6780.55

6848.19

6915.12

6981.34

7046.81

7111.52

7175.44

7238.57

7300.88

7362.34

5

3390.27

3424.09

3457.56

3490.67

3523.40

3555.76

3587.72

3619.28

3650.44

3681.17

6

1695.14

1712.05

1728.78

1745.33

1761.70

1777.88

1793.86

1809.64

1825.22

1840.59

7

847.569

856.023

864.390

872.667

880.851

888.939

896.930

904.821

912.609

920.293

8

423.784

428.012

432.195

436.333

440.425

444.470

448.465

452.411

456.305

460.146

9

211.892

214.006

216.098

218.167

220.213

222.235

224.233

226.205

228.152

230.073

10

105.946

107.003

108.049

109.083

110.106

111.117

112.116

113.103

114.076

115.037

11

52.9730

53.5015

54.0244

54.5417

55.0532

55.5587

56.0581

56.5513

57.0381

57.5183

12

26.4865

26.7507

27.0122

27.2708

27.5266

27.7794

28.0291

28.2757

28.5190

28.7592

13

13.2433

13.3754

13.5061

13.6354

13.7633

13.8897

14.0145

14.1378

14.2595

14.3796

14

6.62163

6.68768

6.75305

6.81771

6.88165

6.94484

7.00727

7.06892

7.12976

7.18979

15

3.31081

3.34384

3.37652

3.40886

3.44082

3.47242

3.50363

3.53446

3.56488

3.59489

16

1.65541

1.67192

1.68826

1.70443

1.72041

1.73621

1.75182

1.76723

1.78244

1.79745

17

0.827704

0.835960

0.844131

0.852214

0.860206

0.868105

0.875909

0.883614

0.891220

0.898724

18

0.413852

0.417980

0.422066

0.426107

0.430103

0.434052

0.437954

0.441807

0.445610

0.449362

19

0.206926

0.208990

0.211033

0.213053

0.215051

0.217026

0.218977

0.220904

0.222805

0.224681

20

0.103463

0.104495

0.105516

0.106527

0.107526

0.108513

0.109489

0.110452

0.111403

0.112340

21

0.0517315

0.0522475

0.0527582

0.0532634

0.0537629

0.0542566

0.0547443

0.0552259

0.0557013

0.0561702

22

0.0258657

0.0261238

0.0263791

0.0266317

0.0268814

0.0271283

0.0273721

0.0276130

0.0278506

0.0280851

23

0.0129329

0.0130619

0.0131895

0.0133158

0.0134407

0.0135641

0.0136861

0.0138065

0.0139253

0.0140426

24

0.00646644

0.00653094

0.00659477

0.00665792

0.00672036

0.00678207

0.00684304

0.00690324

0.00696266

0.00702128

Table 4: Tiled polar stereographic zoom-levels scale sets

 

n

40°

41°

42°

43°

44°

45°

46°

47°

48°

49°

0

118767

119723

120664

121591

122503

123400

124281

125147

125997

126830

1

59383.6

59861.5

60332.2

60795.6

61251.6

61700.0

62140.6

62573.5

62998.3

63415.0

2

29691.8

29930.7

30166.1

30397.8

30625.8

30850.0

31070.3

31286.7

31499.2

31707.5

3

14845.9

14965.4

15083.0

15198.9

15312.9

15425.0

15535.2

15643.4

15749.6

15853.8

4

7422.95

7482.69

7541.52

7599.45

7656.45

7712.50

7767.58

7821.68

7874.79

7926.88

5

3711.48

3741.34

3770.76

3799.73

3828.22

3856.25

3883.79

3910.84

3937.39

3963.44

6

1855.74

1870.67

1885.38

1899.86

1914.11

1928.12

1941.90

1955.42

1968.70

1981.72

7

927.869

935.336

942.691

949.931

957.056

964.062

970.948

977.710

984.349

990.860

8

463.935

467.668

471.345

474.966

478.528

482.031

485.474

488.855

492.174

495.430

9

231.967

233.834

235.673

237.483

239.264

241.016

242.737

244.428

246.087

247.715

10

115.984

116.917

117.836

118.741

119.632

120.508

121.368

122.214

123.044

123.857

11

57.9918

58.4585

58.9182

59.3707

59.8160

60.2539

60.6842

61.1069

61.5218

61.9287

12

28.9959

29.2292

29.4591

29.6854

29.9080

30.1269

30.3421

30.5535

30.7609

30.9644

13

14.4980

14.6146

14.7295

14.8427

14.9540

15.0635

15.1711

15.2767

15.3804

15.4822

14

7.24898

7.30731

7.36477

7.42134

7.47700

7.53174

7.58553

7.63836

7.69022

7.74109

15

3.62449

3.65366

3.68239

3.71067

3.73850

3.76587

3.79276

3.81918

3.84511

3.87055

16

1.81224

1.82683

1.84119

1.85533

1.86925

1.88293

1.89638

1.90959

1.92256

1.93527

17

0.906122

0.913414

0.920596

0.927667

0.934625

0.941467

0.948191

0.954795

0.961278

0.967636

18

0.453061

0.456707

0.460298

0.463834

0.467312

0.470733

0.474096

0.477398

0.480639

0.483818

19

0.226531

0.228353

0.230149

0.231917

0.233656

0.235367

0.237048

0.238699

0.240319

0.241909

20

0.113265

0.114177

0.115075

0.115958

0.116828

0.117683

0.118524

0.119349

0.120160

0.120955

21

0.0566326

0.0570884

0.0575373

0.0579792

0.0584141

0.0588417

0.0592619

0.0596747

0.0600799

0.0604773

22

0.0283163

0.0285442

0.0287686

0.0289896

0.0292070

0.0294208

0.0296310

0.0298374

0.0300399

0.0302386

23

0.0141582

0.0142721

0.0143843

0.0144948

0.0146035

0.0147104

0.0148155

0.0149187

0.0150200

0.0151193

24

0.00707908

0.00713605

0.00719216

0.00724740

0.00730176

0.00735521

0.00740774

0.00745934

0.00750998

0.00755966

n

50°

51°

52°

53°

54°

55°

56°

57°

58°

59°

0

127647

128447

129230

129996

130745

131476

132189

132883

133560

134218

1

63823.5

64223.6

64615.2

64998.2

65372.5

65737.9

66094.4

66441.7

66779.9

67108.9

2

31911.8

32111.8

32307.6

32499.1

32686.2

32869.0

33047.2

33220.9

33390.0

33554.4

3

15955.9

16055.9

16153.8

16249.6

16343.1

16434.5

16523.6

16610.4

16695.0

16777.2

4

7977.94

8027.95

8076.90

8124.78

8171.56

8217.24

8261.79

8305.22

8347.49

8388.61

5

3988.97

4013.98

4038.45

4062.39

4085.78

4108.62

4130.90

4152.61

4173.75

4194.30

6

1994.48

2006.99

2019.23

2031.19

2042.89

2054.31

2065.45

2076.30

2086.87

2097.15

7

997.242

1003.49

1009.61

1015.60

1021.45

1027.15

1032.72

1038.15

1043.44

1048.58

8

498.621

501.747

504.806

507.799

510.723

513.577

516.362

519.076

521.718

524.288

9

249.311

250.873

252.403

253.899

255.361

256.789

258.181

259.538

260.859

262.144

10

124.655

125.437

126.202

126.950

127.681

128.394

129.091

129.769

130.430

131.072

11

62.3276

62.7184

63.1008

63.4748

63.8403

64.1972

64.5453

64.8845

65.2148

65.5360

12

31.1638

31.3592

31.5504

31.7374

31.9202

32.0986

32.2726

32.4423

32.6074

32.7680

13

15.5819

15.6796

15.7752

15.8687

15.9601

16.0493

16.1363

16.2211

16.3037

16.3840

14

7.79095

7.83980

7.88760

7.93435

7.98004

8.02465

8.06816

8.11056

8.15185

8.19200

15

3.89548

3.91990

3.94380

3.96718

3.99002

4.01232

4.03408

4.05528

4.07592

4.09600

16

1.94774

1.95995

1.97190

1.98359

1.99501

2.00616

2.01704

2.02764

2.03796

2.04800

17

0.973869

0.979974

0.985950

0.991794

0.997505

1.00308

1.00852

1.01382

1.01898

1.02400

18

0.486935

0.489987

0.492975

0.495897

0.498752

0.501540

0.504260

0.506910

0.509491

0.512000

19

0.243467

0.244994

0.246487

0.247949

0.249376

0.250770

0.252130

0.253455

0.254745

0.256000

20

0.121734

0.122497

0.123244

0.123974

0.124688

0.125385

0.126065

0.126728

0.127373

0.128000

21

0.0608668

0.0612484

0.0616219

0.0619871

0.0623441

0.0626925

0.0630325

0.0633638

0.0636863

0.0640000

22

0.0304334

0.0306242

0.0308109

0.0309936

0.0311720

0.0313463

0.0315162

0.0316819

0.0318432

0.0320000

23

0.0152167

0.0153121

0.0154055

0.0154968

0.0155860

0.0156731

0.0157581

0.0158409

0.0159216

0.0160000

24

0.00760835

0.00765605

0.00770273

0.00774839

0.00779301

0.00783657

0.00787906

0.00792047

0.00796079

0.00800000

Table 4: Tiled polar stereographic zoom-levels scale sets

 

n

60°

61°

62°

63°

64°

65°

66°

67°

68°

69°

0

134857

135477

136078

136659

137221

137764

138286

138789

139271

139733

1

67428.4

67738.4

68038.9

68329.7

68610.7

68881.9

69143.1

69394.3

69635.4

69866.3

2

33714.2

33869.2

34019.5

34164.8

34305.4

34440.9

34571.5

34697.1

34817.7

34933.1

3

16857.1

16934.6

17009.7

17082.4

17152.7

17220.5

17285.8

17348.6

17408.8

17466.6

4

8428.55

8467.31

8504.86

8541.21

8576.34

8610.23

8642.89

8674.29

8704.42

8733.29

5

4214.27

4233.65

4252.43

4270.61

4288.17

4305.12

4321.44

4337.14

4352.21

4366.64

6

2107.14

2116.83

2126.22

2135.30

2144.08

2152.56

2160.72

2168.57

2176.11

2183.32

7

1053.57

1058.41

1063.11

1067.65

1072.04

1076.28

1080.36

1084.29

1088.05

1091.66

8

526.784

529.207

531.554

533.826

536.021

538.140

540.180

542.143

544.026

545.830

9

263.392

264.603

265.777

266.913

268.011

269.070

270.090

271.071

272.013

272.915

10

131.696

132.302

132.888

133.456

134.005

134.535

135.045

135.536

136.007

136.458

11

65.8480

66.1508

66.4442

66.7282

67.0026

67.2674

67.5225

67.7679

68.0033

68.2288

12

32.9240

33.0754

33.2221

33.3641

33.5013

33.6337

33.7613

33.8839

34.0016

34.1144

13

16.4620

16.5377

16.6111

16.6821

16.7507

16.8169

16.8806

16.9420

17.0008

17.0572

14

8.23101

8.26885

8.30553

8.34103

8.37533

8.40843

8.44032

8.47098

8.50041

8.52860

15

4.11550

4.13443

4.15277

4.17051

4.18767

4.20422

4.22016

4.23549

4.25021

4.26430

16

2.05775

2.06721

2.07638

2.08526

2.09383

2.10211

2.11008

2.11775

2.12510

2.13215

17

1.02888

1.03361

1.03819

1.04263

1.04692

1.05105

1.05504

1.05887

1.06255

1.06608

18

0.514438

0.516803

0.519096

0.521314

0.523458

0.525527

0.527520

0.529436

0.531276

0.533038

19

0.257219

0.258402

0.259548

0.260657

0.261729

0.262763

0.263760

0.264718

0.265638

0.266519

20

0.128609

0.129201

0.129774

0.130329

0.130865

0.131382

0.131880

0.132359

0.132819

0.133259

21

0.0643047

0.0646004

0.0648870

0.0651643

0.0654323

0.0656909

0.0659400

0.0661795

0.0664095

0.0666297

22

0.0321524

0.0323002

0.0324435

0.0325821

0.0327161

0.0328454

0.0329700

0.0330898

0.0332047

0.0333148

23

0.0160762

0.0161501

0.0162217

0.0162911

0.0163581

0.0164227

0.0164850

0.0165449

0.0166024

0.0166574

24

0.00803809

0.00807505

0.00811087

0.00814553

0.00817903

0.00821136

0.00824250

0.00827244

0.00830118

0.00832871

n

70°

71°

72°

73°

74°

75°

76°

77°

78°

79°

0

140174

140595

140995

141374

141732

142069

142384

142679

142951

143203

1

70087.0

70297.3

70497.3

70686.8

70865.8

71034.3

71192.1

71339.3

71475.7

71601.4

2

35043.5

35148.7

35248.6

35343.4

35432.9

35517.1

35596.0

35669.6

35737.9

35800.7

3

17521.7

17574.3

17624.3

17671.7

17716.5

17758.6

17798.0

17834.8

17868.9

17900.3

4

8760.87

8787.16

8812.16

8835.85

8858.23

8879.28

8899.01

8917.41

8934.46

8950.17

5

4380.44

4393.58

4406.08

4417.93

4429.11

4439.64

4449.51

4458.70

4467.23

4475.09

6

2190.22

2196.79

2203.04

2208.96

2214.56

2219.82

2224.75

2229.35

2233.62

2237.54

7

1095.11

1098.40

1101.52

1104.48

1107.28

1109.91

1112.38

1114.68

1116.81

1118.77

8

547.554

549.198

550.760

552.241

553.639

554.955

556.188

557.338

558.404

559.386

9

273.777

274.599

275.380

276.120

276.820

277.478

278.094

278.669

279.202

279.693

10

136.889

137.299

137.690

138.060

138.410

138.739

139.047

139.334

139.601

139.846

11

68.4443

68.6497

68.8450

69.0301

69.2049

69.3694

69.5235

69.6672

69.8005

69.9232

12

34.2222

34.3249

34.4225

34.5150

34.6024

34.6847

34.7618

34.8336

34.9002

34.9616

13

17.1111

17.1624

17.2113

17.2575

17.3012

17.3423

17.3809

17.4168

17.4501

17.4808

14

8.55554

8.58122

8.60563

8.62876

8.65061

8.67117

8.69044

8.70840

8.72506

8.74040

15

4.27777

4.29061

4.30281

4.31438

4.32531

4.33559

4.34522

4.35420

4.36253

4.37020

16

2.13888

2.14530

2.15141

2.15719

2.16265

2.16779

2.17261

2.17710

2.18127

2.18510

17

1.06944

1.07265

1.07570

1.07860

1.08133

1.08390

1.08631

1.08855

1.09063

1.09255

18

0.534721

0.536326

0.537852

0.539298

0.540663

0.541948

0.543153

0.544275

0.545316

0.546275

19

0.267361

0.268163

0.268926

0.269649

0.270332

0.270974

0.271576

0.272138

0.272658

0.273138

20

0.133680

0.134081

0.134463

0.134824

0.135166

0.135487

0.135788

0.136069

0.136329

0.136569

21

0.0668401

0.0670407

0.0672315

0.0674122

0.0675829

0.0677436

0.0678941

0.0680344

0.0681645

0.0682844

22

0.0334201

0.0335204

0.0336157

0.0337061

0.0337915

0.0338718

0.0339470

0.0340172

0.0340823

0.0341422

23

0.0167100

0.0167602

0.0168079

0.0168530

0.0168957

0.0169359

0.0169735

0.0170086

0.0170411

0.0170711

24

0.00835502

0.00838009

0.00840393

0.00842652

0.00844786

0.00846794

0.00848676

0.00850430

0.00852057

0.00853555

Table 4: Tiled polar stereographic zoom-levels scale sets

 

n

80°

81°

82°

83°

84°

85°

0

143433

143641

143827

143992

144134

144255

1

71716.3

71820.4

71913.6

71995.9

72067.2

72127.7

2

35858.1

35910.2

35956.8

35997.9

36033.6

36063.8

3

17929.1

17955.1

17978.4

17999.0

18016.8

18031.9

4

8964.54

8977.54

8989.19

8999.48

9008.41

9015.96

5

4482.27

4488.77

4494.60

4499.74

4504.20

4507.98

6

2241.13

2244.39

2247.30

2249.87

2252.10

2253.99

7

1120.57

1122.19

1123.65

1124.94

1126.05

1126.99

8

560.284

561.097

561.825

562.468

563.025

563.497

9

280.142

280.548

280.912

281.234

281.513

281.749

10

140.071

140.274

140.456

140.617

140.756

140.874

11

70.0354

70.1371

70.2281

70.3085

70.3782

70.4372

12

35.0177

35.0685

35.1140

35.1542

35.1891

35.2186

13

17.5089

17.5343

17.5570

17.5771

17.5945

17.6093

14

8.75443

8.76713

8.77851

8.78856

8.79727

8.80465

15

4.37722

4.38357

4.38926

4.39428

4.39864

4.40232

16

2.18861

2.19178

2.19463

2.19714

2.19932

2.20116

17

1.09430

1.09589

1.09731

1.09857

1.09966

1.10058

18

0.547152

0.547946

0.548657

0.549285

0.549829

0.550291

19

0.273576

0.273973

0.274328

0.274642

0.274915

0.275145

20

0.136788

0.136986

0.137164

0.137321

0.137457

0.137573

21

0.0683940

0.0684932

0.0685821

0.0686606

0.0687287

0.0687863

22

0.0341970

0.0342466

0.0342911

0.0343303

0.0343643

0.0343932

23

0.0170985

0.0171233

0.0171455

0.0171652

0.0171822

0.0171966

24

0.00854925

0.00856165

0.00857276

0.00858258

0.00859108

0.00859829

n

86°

87°

88°

89°

90°

0

144354

144431

144486

144519

144530

1

72177.2

72215.7

72243.2

72259.7

72265.2

2

36088.6

36107.8

36121.6

36129.8

36132.6

3

18044.3

18053.9

18060.8

18064.9

18066.3

4

9022.14

9026.96

9030.40

9032.46

9033.15

5

4511.07

4513.48

4515.20

4516.23

4516.57

6

2255.54

2256.74

2257.60

2258.11

2258.29

7

1127.77

1128.37

1128.80

1129.06

1129.14

8

563.884

564.185

564.400

564.529

564.572

9

281.942

282.092

282.200

282.264

282.286

10

140.971

141.046

141.100

141.132

141.143

11

70.4855

70.5231

70.5500

70.5661

70.5715

12

35.2428

35.2615

35.2750

35.2830

35.2857

13

17.6214

17.6308

17.6375

17.6415

17.6429

14

8.81069

8.81539

8.81875

8.82076

8.82143

15

4.40534

4.40769

4.40937

4.41038

4.41072

16

2.20267

2.20385

2.20469

2.20519

2.20536

17

1.10134

1.10192

1.10234

1.10260

1.10268

18

0.550668

0.550962

0.551172

0.551298

0.551340

19

0.275334

0.275481

0.275586

0.275649

0.275670

20

0.137667

0.137740

0.137793

0.137824

0.137835

21

0.0688335

0.0688702

0.0688964

0.0689122

0.0689174

22

0.0344167

0.0344351

0.0344482

0.0344561

0.0344587

23

0.0172084

0.0172176

0.0172241

0.0172280

0.0172294

24

0.00860419

0.00860878

0.00861206

0.00861402

0.00861468